# Frank Solutions for Chapter 1 Measurement Class 9 Physics ICSE

**Exercise 1.1**

**1. What is meant by measurement?**

**Answer**

Measurement is an act or the result of comparison of a quantity whose magnitude is unknown with a predefined standard.

**2. Define a fundamental quantity.**

**Answer**

The physical quantities like mass, length and time which do not depend on each other are known as fundamental quantities.

**3. Name the three fundamental quantities.**

**Answer**

Length, mass, time are the three fundamental quantities.

**4. What do you mean by the term unit?**

**Answer**

Unit is a standard quantity of the same kind with which a physical quantity is compared for measuring it.

**5. Define standard meter.**

**Answer**

A standard metre is equal to 1650763.73 wavelengths in vacuum, of the radiation from krypton isotope of mass 86.

**6. Name three systems of unit and state various fundamental units in them.**

**Answer**

Three systems of unit are

- C.G.S system - fundamental unit of length is centimetre(cm), of mass is gram(gm), of time is second(s).
- F.R.S system - fundamental unit of length is foot(ft), of mass is pound(|b), of time is second(s).
- M.K.S system- fundamental unit of length is metre(m), of mass is kilogram(kg), of time is second(s).

**7. Name the SI unit of mass and define it.**

**Answer**

The SI unit of mass is Kilogram. One standard kilogram is equal to the mass of a cylinder of nearly same height and diameter and made up of platinum and iridium alloy.

**8. Name three units of length which are bigger than a meter. How are they related to the meter?**

**Answer**

Three units of length greater than a metre are

- Decameter = 10 metre
- Hectometer = 100 metre
- Kilometer = 1000 metre

**9. What are the fundamentals units in SI system? Name them along with their symbols. **

**Answer**

Fundamental units in SI system are

**10. What do you mean by light year?**

**Answer**

Light year is defined as the distance travelled by light in vacuum in one year.

**11. Write the name and relationship of two units of length smaller than a meter.**

**Answer**

Two units of length smaller than a metre are

- Decimeter = 0.1 metre
- Centimeter = 0.01 metre

**12. Which of the following is not a unit of distance?**

**(a) Leap year**

**(b) parsec**

**(c) light year**

**(d) Angstrom**

**Answer**

(a) Leap year because it is a unit of time

**13. What is meant by order of magnitude of a physical quantity? Give two examples.**

**Answer**

Order of magnitude of a physical quantity is defined as its magnitude in powers of ten when that physical quantity is expressed in powers of ten with one digit towards the left decimal.

For example, volume = 52.37 m^{3} then the order of magnitude is 10^{2}m^{3}.

**14. Is micron same as millimeter?**

**Answer**

No, micron is not same as millimeter because micron is equal to 10^{-6} metre while a millimeter is equal to 10^{-3} metre

**15. Complete the following:**

**(i) 1 fermi = _____ m**

**(ii) 1 m = _____** **Ã…**

**(iii) 1 parsec = ______ 1y**

**(iv) 1 light year = ______ m**

**(v) 1 m = _____ ****Î¼**

**(vi) 1 micron = ______ ****Ã…**

**(vii) 1 u = ______ kg**

**Answer**

(i)** **1 fermi = 10^{-15} m

(ii) 1 m = 10^{10} Ã…

(iii) 1 parsec = 3.261y

(iv) 1 light year = 9.46×10^{15} m

(v) 1 m = 10^{6} Î¼

(vi) 1 micron = 10^{4} Ã…

(vii) 1 u = 1.655 × 10^{-27} kg

**16. State two units of mass smaller than a kilogram?**

**Answer**

Two units of mass smaller than a kilogram are

- Gram = 10
^{-3}Kg - Miligram = 10
^{-6}Kg

**17. What is a leap year ? **

**Answer**

A leap year refers to a year in which February has 29 days and the total days in the year are 366 days.

**18. The wavelength of a particular colour is 5400 Ã…. Express it in nanometer and metre. **

**Answer**

1 Ã… = 10^{-1} nm

So, 5400 Ã… = 5400×10^{-1} = 540 nm

1 Ã… = 10^{-10} m

So, 5400 Ã… = 5400×10^{-10 }= 5.4×10^{-7 }m

**19. The size of bacteria is 2Î¼. Find the number of bacteria in 3 m length.**

**Answer**

1 Î¼ = 10^{-8} m

Length of one bacteria = 2 Î¼ = 2×10^{-6} m

Length given = 3m

Number of bacteria = length given/length of one bacteria

= 3/(2×10^{-6})

= 15×10^{8}

**20. Complete the following: **

**(i) 1 quintal = ______ kg **

**(ii) 1 mg = _____kg **

**(iii) 1 mean solar day = ****_____**** s **

**(iv) 1 nano second = ****_____**** s **

**(v) 1 year = ****_____**** s **

**Answer: **

(i) quintal = 100 kg

(ii) 1 mg = 10^{-6} kg

(iii) 1 mean solar day = 86400 s

(iv) 1 nano second = 10^{-9} s

(v) 1 year = 3.15×10^{7} s

**Exercise 1.2 **

**1. What do you mean by the term pitch of a screw gauge?**

**Answer**

When one complete rotation is given to the screw hand, it moves forward or backward by a distance is called pitch of the screw. It is distance between two consecutive threads of the screw.

Pitch of the screw = distance travelled by screw in n rotations/n rotations

**2. Is pitch same as least count?**

**Answer**

No, least count is not same as pitch because least count is found by dividing pitch by number of divisions on the circular scale.

**3. ****State two uses of vernier calipers.**

**Answer**

Two uses of vernier caliper are

- Measuring the internal diameter of a tube or a cylinder.
- Measuring the length of an object.

**4. State two limitations of a metre rule. **

**Answer**

Two limitations of metre rule

- There comes an error of parallax due to thickness of the metre rule.
- We cannot use metre rule for measuring small thickness.

**5. Explain the terms (i) pitch, and (ii) least count of a screw gauge. How are they determined?**

**Answer**

When one complete rotation is given to the screw hand, it moves forward or backward by a distance called pitch of the screw. It is distance between two consecutive threads of the screw.

Pitch of the screw = distance travelled by screw in n rotations/n rotations

Least count refers to the smallest reading that can be accurately measured while using an instrument. The least count is the value of one division on its scale.

**6. While measuring the volume of a piece copper, it is found that the initial level of water in a graduated cylinder is 30 ml and on immersing the piece in water, the level of water rises to 50 ml. Find the volume of the piece of copper.**

**Answer**

Initial level of water in cylinder = 30 ml

Level of water in cylinder after immersing piece of copper = 50 ml

Volume of copper piece = 50-30 = 20 ml

**7. Draw a neat labelled diagram of vernier calipers. **

**Answer**

A well labelled diagram of Vernier caliper is shown in figure

**8. What is the purpose of a ratchet in a screw gauge ? **

**Answer**

The ratchet is used in a screw gauge to hold the object under measurement gently between the studs.

**9. What do you mean by zero error of a screw gauge? How is it accounted for?**

**Answer**

If the zero of the circular scale does not coincide with the zero of the main scale (pitch scale), this is known as zero error. There are two types of zero error -

- If the zero of the circular scale remains below the line of graduation then it is called positive zero error
- If the zero of the circular scale lies above the line of graduation then it is called negative zero error

For positive zero error correction, the zero error should always be subtracted from the observed reading

For negative zero error correction, the zero error must be added to the observed reading.

**10. Name the two scales of a screw gauge.**

**Answer**

Two scales in a screw gauge are

- A linear scale called the main scale graduated in half millimeters
- A circular scale divided into 50 or 100 equal parts.

**11. What is backlash error ? How is it avoided?**

**Answer**

Due to constant use, there is space for the play of screw gauge but gradually this space increases with the use or wear and tear, so that when the screw is moved by rotating it in some direction, it slips in the nut and does not cover any linear distance for some rotation of the screw head. The error due to this is known as backlash error.

It is avoided by turning the screw always in the same direction.

**12. How will you measure the diameter of a wire using a screw gauge?**

**Answer**

Following procedure is used to measure the diameter of a wire

- Calculate the least count and zero error of the screw gauge.
- Place the wire in between the studs. Turn the ratchet clockwise so as to hold the wire gently in between the studs. Record the main scale reading.
- Now record the division of circular scale that coincides with the base line of main scale. This circular scale division multiplied by least count will give circular scale reading.
- The observed diameter is obtained by adding the circular scale reading to the main scale reading. Subtract the zero error if any, with its proper sign, from the observed diameter to get the true diameter.

**13. In fig. 19, the pitch of the screw is 1 mm. Calculate: **

**(i) the least count of screw gauge and **

**(ii) the reading represented in the figure.**

**Answer**

Screw gauge in the figure

(i) Pitch of the screw = 1 mm

Divisions on circular scale= 100

Least count = pitch of the screw/ divisions on the main scale

L.C. = 1/100 = 0.01 mm = 0.001 cm

(ii) LC. = 0.001 cm

the main scale reading = 2 mm = 0.2 cm

from the figure it is clear that base line coincides with the 97^{th} division of the circular scale.

So, circular scale reading = 97 × 0.001 cm = 0.097 cm

Hence, reading shown In the figure = 0.2 + 0.097 = 0.297 cm

**14. Which of the following measures a small length to a high accuracy: metre scale, vernier calipers, screw gauge?**

**Answer**

Screw gauge measures a small length to a high accuracy because it has the lowest least count among the given three instruments. And low least count means high accuracy.

**15. Name the instrument which has the least count**

**(a) 0.1. mm**

**(b) 1 mm**

**(c) 0.01 mm.**

**Answer**

Instruments which have least count as follows

(a) 0.dmm = Vemier calipers

(b) 1 mm = Metre scale

(c) 0.01 mm = Screw gauge

**16. Name the measuring employed to measure**

**(i) The diameter of a needle,**

**(ii) the thickness of a paper and**

**(iii) the diameter of a pencil.**

**Answer**

Measuring employed to measure the following

(i) The diameter of a needle = __Screw Gauge__

(ii) The thickness of a paper = __Screw Gauge__

(iii) The diameter of a pencil = __Screw Gauge__

Because screw gauge is more accurate and can measure the thicknesses which metre scale and Vernier calliper cannot.

**17. While measuring the length of a rod with vernier calipers, fig. 20 shows the position of two scales. Calculate the length of the rod.**

**Answer**Least count of vernier calliper shown in the figure above = 0.01 cm

Main scale reading = 3.3 cm

Vernier scale 6th division is coinciding with main scale division

Hence, vemier scale reading = 6 **×** 0.01 cm = 0.06 cm

Hence, the length of the rod = 3.3 + 0.06 = 3.36cm

**18. What do you mean by a positive zero error of a screw gauge? How will you calculate it?**

**Answer**

If the zero of the circular scale remains below the line of graduation then it is called positive zero error. When there is positive zero error, then the instrument reads more than the actual reading. Therefore in order to get the correct reading, the zero error should always be subtracted from the observed reading.

**19. The pitch of a screw gauge is 0.5 mm and the head scale is divided in 100 parts. What is the least count of screw gauge?**

**Answer**

Pitch of the screw gauge = 0.5mm = 0.05 cm

Circular scale divisions = 100

Least Count of screw gauge = pitch of the gauge/circular scale divisions

= 0.05/100

= 0.0005 cm

**20. What do you mean by a negative zero error of a screw gauge? How will you calculate it?**

**Answer**

If the zero of the circular scale lies above the line of graduation then it is called negative zero error. When there is negative zero error, then the instrument reads less than the actual reading. Therefore in order to get the correct reading, the zero error should always be added to the observed reading.

**21. State whether the following statement is true or false by writing T/F against it.**

**(a) The diameter of a wire can be measured more accurately by using vernier calipers than by a screw gauge.**

**(b) The least count of a screw gauge can be lowered by increasing the number of divisions on its thimble.**

**(c) A metre scale can measure a length 6.346 cm.**

**(d) The ratchet of a screw gauge is used to measure the depth of a beaker.**

**(e) The metre scale, vernier calipers and screw gauge are in decreasing order of least count.**

**Answer**

(a) False, because the accuracy is higher in case of screw gauge due to lower least count value of 0.01mm

(b) True

(c) False, because its least count is limited to 0.1 cm. thus this length can be measured with an instrument of least count of 0.001 cm i.e. screw gauge

(d). False, the ratchet is used to hold the object under measurement gently between the studs.

(e) True

**22. What do you mean by the term volume of a body?**

**Answer**

The space occupied by a body is known as its volume. SI unit of volume is cubic metre (m^{3})

**23. Is 1 cm ^{3} same as 1 ml ?**

**Answer**

Yes, 1 cm^{3} is same as 1 ml.

**24. Express 1 liter in terms m ^{3}.**

**Answer**

1m^{3} = 1000 litre

1 litre = 1/1000 m^{3}

= 0.001 m^{3}

**25. How will you find the volume of an irregular solid (lighter than water) by displacement method ? **

**Answer**

- Fill the graduated cylinder with water.
- Take a heavy solid (eg. piece of metal) insoluble in water. This metal piece is called sinker.
- Tie the sinker to a strong string and lower it into the water gently and record the lower meniscus of water and let the value be V
_{1}. - Now take out the sinker and along with it we the solid whose volume is to be measured and lower them into the water.
- Note the reading carefully and let the value be V;
- Volume of the solid, V = V
_{2}- V_{1}

**26. What is the SI unit of volume? How is it related to liter?**

**Answer**

SI unit of volume is cubic metre or metre^{3} (m^{3}).

The relation between liter and metre^{3}

1 metre^{3} = 1000 liter

**27. A screw has a pitch equal to 0.5 mm. What should be the number of divisions on its head so as to read correct upto 0.001 mm with its help ? **

**Answer**

Pitch of the screw = 0.5 mm

Least count = 0.001 mm

Number of divisions = pitch/least count

= 0.5/0.001

= 500

**28. Fig. 21 shows the reading obtained while measuring the diameter of a wire using a screw gauge. The screw advances by 1 ****division on the main scale when the circular head is rotated once.**

**Calculate:**

**(i) pitch of the screw gauge,**

**(ii) Least count of the screw gauge, and**

**(iii) The diameter of the wire.**

**Answer**

So, pitch of the screw = 1mm

Number of divisions = 50

Least count = pitch/number of divisions

= 1/50 = 0.02 mm

Now for the reading shown in figure,

The main scale reading = 4mm

From the figure it is dear that base line coincides with the 47" division of the circular scale.

So, circular scale reading = 47 × 0.02 mm = 0.94 cm

Hence, reading shown in the figure = 4 + 0.94 = 4.94 cm

**29. State three precautions you would take while measuring the volume of an irregular solid lighter than water, using a measuring cylinder.**

**Answer**

Precautions to be taken while measuring volume of a solid lighter than water using displacement method

- The sinker should be insoluble in water
- The sinker should have a high density than water.
- Lower meniscus should be read to note down the readings and error due to parallax should be avoided.

**30. How will you find the volume of a lump of salt or sugar using a graduated cylinder?**

**Answer**

Measurement of volume of an irregular solid soluble in water using a graduated cylinder.

- In this case, kerosene or any liquid whose density is lighter than water and in which the solid is not soluble is used.
- Fill the graduated cylinder with the liquid.
- Record the lower meniscus of liquid and let the value be V
_{1}. - Tie the solid whose volume is to be measured to a strong string and lower it into the water gently.
- Note the reading carefully and let the value be V
_{2} - Volume of the solid, V = V
_{2}– V_{1}

**Exercise 1.3 **

**1. What do you mean by a simple pendulum?**

**Answer**

A simple pendulum consists a heavy point mass (called the bob) suspended by a mass less and an Inextensible or non-elastic thread from a fixed point or rigid support**.**

**2. What is a seconds pendulum?**

**Answer**

A seconds pendulum is a pendulum which takes 2 seconds to complete one oscillation. The length of seconds pendulum, where g = 9.8ms^{-2}, is nearly 1m.

**3. Name a device used to measure the short intervals of time.**

**Answer**

A stopwatch is used to measure short intervals of time.

**4. Write the SI unit of frequency?**

**Answer**

Sl unit of frequency is hertz (Hz).

**5. Define one hertz.**

**Answer**

When a pendulum completes one oscillation in one second, then the frequency is one hertz.

**6. State the relation between frequency and time period.**

**Answer**

The time period, T and frequency of oscillation, f are related as,

T = 1/f or f = 1/T

**7. What do you mean by an oscillation? Is there any relation between oscillation and amplitude?**

**Answer**

One complete to and fro motion of a pendulum about its mean position is known as oscillation. Amplitude is the magnitude of the maximum displacement of the bob from the mean position on either side when an oscillation takes place.

**8. Write the SI unit of amplitude.**

**Answer**

Sl unit of amplitude is metre (m).

**9. What is a seconds pendulum?**

**Answer**

A seconds pendulum is a pendulum which takes 2 seconds to complete one oscillation. The length of second pendulum, where g = 9.8 ms^{-2}, is nearly 1 m.

**10. Calculate the length of a seconds pendulum at a place where g = 9.8 ms- ^{2}.**

**Answer**

**11. A person sitting on a swing stands up. The time period of swing : **

**(a) Increases **

**(b) Decreases **

**(c) Does not change **

**(d) become zero. **

**Answer**

The time period of swing decreases because in the standing position, the centre of the mass of the person shifts upwards. Due to which the effective length of the pendulum, l decreases. As Î± √l, therefore time decreases.

**12. Moon has no atmosphere and acceleration due to gravity at its surface is one-sixth that at the earth surface. When a pendulum is taken from earth to moon surface, its time period will:**

**(a) Increase**

**(b) decrease**

**(c) Not change**

**(d) becomes infinite.**

**Answer**

When a pendulum is taken from earth to moon surface, its time period will increase because the acceleration due to gravity on moon is less than that on earth and the time period depends inversely on square root of acceleration due to gravity.

**13. The time period of a pendulum is infinite. What will happen to its oscillation?**

**Answer**

If time period of a pendulum becomes infinite, the pendulum will not oscillate at all as pendulum will take infinite time to complete one oscillation.

**14. What do you mean by the effective length of a simple pendulum?**

**Answer**

Effective length of a simple pendulum is the distance of the point of oscillation (i.e. the centre of the gravity of bob) from the point of suspension.

**15. Draw a graph of I against T ^{2 }for a simple pendulum of length | and time period T for different values of l.**

**Answer**

A graph of l against T^{2} for a simple pendulum of length l and time period T is shown in the figure

**16. Name the factors on which the time period of a simple pendulum depends. Write the formula for the time period in terms of the above named factors.**

**Answer**

The time period of simple pendulum is directly proportional to the square root of the length of the pendulum

The time period of simple pendulum is inversely proportional to the square root of acceleration due to gravity

Where T is the time period,

l is the length of the pendulum,

g is acceleration due to gravity.

**17. Compare the time periods of a simple pendulum at places where g = 9.8 ms ^{-2} and 4.36 ms^{-2} respectively.**

**Answer: **

g_{1} = 9.8 ms^{-2}

g_{2 }= 4.36ms^{-2}

**18. Does the time period of a simple pendulum depend on the mass of the bob?**

**Answer**

The time period of a pendulum is independent of mass of the bob.

**19. The time periods of two simple pendulums at a place are in the ratio 2 : 1. What will be the corresponding ratio of their lengths?**

**Answer**

**20. What do you mean by mass? Name the instrument used to measure the mass of a body.**

**Answer**

The quantity of matter contained Mass of a body can be measured by using a beam balance. In a body is called its mass. Mass is always constant for a given body.

**21. What is the principle of a beam balance?**

**Answer**

A beam balance works on the principle of moments. According to the principle of moments, under equilibrium condition, the clockwise moment due to the body on one side of beam equals the anti clockwise moment due to standard weights on the other side of beam.

**22. State important precautions employed for measuring the mass of a body using a beam balance.**

**Answer**

Precautions to be taken to measure the mass of a body using beam balance are

- The beam must be gently lowered before adding or removing weights from the pan.
- The weights should not be carried with bare hands to avoid the change in weights due to moisture and dust particles from the surrounding.
- The lever should be turned gently, in order to prevent knife edges from chipping.
- Never keep the wet or hot objects on the pan.
- The weights should be placed into weight box after use.
- Whenever you are near the actual weight, you should carefully try the weights in the descending order.

**23. Write the SI units of time and mass.**

**Answer**

Sl units of time and mass are second (s) and kilogram (kg) respectively.

**24. What are the conditions for a beam balance to be true?**

**Answer**

Conditions for a beam balance to be true are

(a) Both the pans must be of equal weights.

(b) Both the arms must be of equal lengths.

**Exercise 1.4**

**1. Define least count of an instrument.**

**Answer**

Least count of an instrument refers to the smallest reading that can be accurately measured while using the instrument. For an instrument provided with a scale the least count is the value of one division on its scale.

**2. What is the maximum possible error in the measurement of 1.80 cm?**

**Answer**

Maximum possible error is 0.1 cm.

**3. What do you mean by the slope of a graph?**

**Answer**

Slope of a graph identifies the proportional relationship between the quantities plotted.

**4. What is the least count in case of the following instruments?**

**(i) Metre scale**

**(ii) vernier calipers**

**(iii) Screw gauge**

**Answer**

Least count of the following are

(i) Metre scale = __0.1__ cm

(ii) Vernier calipers = __0.01__ cm

(iii) Screw gauge = __0.001__ cm

**5. What is the least count in case of the following instruments?**

**(i) Stopwatch**

**(ii) Thermometer**

**(iii) Spring balance**

**Answer**

Least count of the following are

(i) Stopwatch = __0.1__ s

(ii) Thermometer = __0.1 °C__

(iii) Spring balance = __1 gm wt__

**6. ‘Each measuring instrument has a limit of accuracy’. Comment on the statement.**

**Answer**

Accuracy is the extent to which a reported measurement approaches the true value of the quantity measured. This extent is usually described by the least count of the instrument and since the least count for a given instrument is limited hence, the accuracy of the instrument is limited.

**7. Name two kinds of error in a measurement. How are they minimized ? **

**Answer**

Two types of error in a measurement are

- Random errors-these errors are due to various factors. In a number of observations we get different readings every time. These errors can be minimized by taking observations a large number of times and taking the arithmetic mean of the readings.
- Gross error- these errors are due to carelessness of the observer like parallax, improper setting of the instrument.

These errors can be minimized only when the observer is careful in setting up of instrument and taking readings.

**8. Which of the following measurement is most accurate?**

**(a) 3000 g**

**(b) 3.0 kg**

**(c) 3.00 kg**

**(4) 3 kg**

**Answer**

3000g is the most accurate measurement because it has maximum number of significant figures = 4.

**9. Is there any difference in the following measurements?**

**(a) 51.7 cm**

**(b) 51.70 cm**

**(c) 51.700 cm.**

**Explain your answer.**

**Which measurement is most accurate?**

**Answer**

Basically there is no difference between the quantity being measured but there is a difference of significant figures in the measurement.

(a) Number of significant figures = 3

(b) Number of significant figures = 4

(c) Number of significant figures = 5

Since (c) part has maximum number of significant figures = 5, therefore it is most accurate among the given three.

**Exercise 1.5**

**1. What is meant by a unit?**

**Answer**

Unit is a standard quantity of the same kind with which a physical quantity is compared for measuring it.

**2. What are fundamental units?**

**Answer**

The units which can neither be derived from one another, nor can they be further resolved into other units are known as fundamental units.

**3. What are derived units?**

**Answer**

The units which can be expressed in terms of fundamental units of mass, length and time are known as derived units.

**4. Define standard meter.**

**Answer**

A standard metre is equal to 1650763.31 wavelengths in vacuum, of the radiation from krypton isotope of mass 86.

**5. Define standard kilogram.**

**Answer**

One standard kilogram ig equal to the mass of a cylinder of nearly same height and diameter and made up of platinum and iridium alloy.

**6. Name the SI unit of electric current.**

**Answer**

SI unit of electric current is Ampere (A)

**7. Define light year.**

**Answer**

Light year is defined as the distance travelled by light in vacuum in one year.

**8. Which is bigger: light year or parsec?**

**Answer**

1 Parsec is bigger because 1 Parsec is 3.26 times a light year.

**9. Which is smaller: micron or Fermi?**

**Answer**

1 Fermi is smaller because 1 Fermi is 10^{-15} m while 1 micron is 10^{-6} m.

**10. Define parsec. Is it same as Astronomical unit?**

**Answer**

Parsec refers to the distance at which an arc of length equal to 1 astronomical unit subtends an angle of one second at a point.

No, parsec is not same as astronomical unit (A.U.).

1 Parsec = 2×10^{5} A.U.

**11. What is the least count of your laboratory Vernier calipers ?**

**Answer**

Least count of a Vernier caliper used in laboratory is 0.1mm = 0.01cm

**12. What is the importance of a Vernier scale?**

**Answer**

Vernier caliper is an instrument used for measuring small lengths of solid objects where an ordinary scale cannot be applied. We can measure the length accurately up to the order of 10^{-2} cm, 10^{-3 }cm depending upon the Vernier used. Therefore a Vernier caliper is important to measure the fraction of a smallest division of a measuring scale which otherwise could not be done by the judgment of the eye.

**13. Define least count of an instrument.**

**Answer**

Least count of an instrument refers to the smallest reading that can be accurately measured while using the instrument. For an instrument provided with a scale the least count is the value of one division on its scale.

**14. Can we measure the thickness of a piece of paper by Vernier calipers ? **

**Answer**

No, we cannot measure the thickness of a paper with Vernier caliper as its least count is only 0.1 mm. We should use screw gauge instead as its least court is 0.01 mm as the thickness of the paper is in the range of 10^{2} mm.

**15. How does the zero error arise in the instrument?**

**Answer**

If the zero of the one scale (Vernier scale or circular scale of screw gauge) does not coincide with the zero of the main scale, this is known as zero scale, zero error arises. There are two types of zero error -

- If the zero of the scale remains below the line of graduation of the main scale then it is called positive zero error
- If the zero of the scale lies above the line of graduation of the main scale then it is called negative zero error

**16. Why is the screw gauge so named?**

**Answer**

Screw gauge consists essentially of a screw with a uniform pitch which moves in a nut, thus it is named as screw gauge because the major working part is a screw.

**17. Define the time period of a simple pendulum. **

**Answer**

The time taken by a simple pendulum for an oscillation is known as the time period of a simple pendulum.

Where T is the time period,

l is the of the pendulum,

g is acceleration due to gravity

**18. How does the presentation of data in a tabular form help us in analysing them? Explain with one example.**

**Answer**

The presentation of the data in a tabular form helps in quick grasping and analyzing the recorded observations. For example to measure a diameter using a vernier caliper we record the following data in a tabular form as follows

**19. Name the material used for making a screw gauge.**

**Answer**

Material used for making screw gauge is stainless steel to avoid expansion and contraction due to change in weather as stainless steel absorbs a little heat.

**20. Define pitch of the screw gauge.**

**Answer**

When one complete rotation is given to the screw hand, it moves forward or backward by a distance is called pitch of the screw. It is distance between two consecutive threads of the screw.

Pitch of the screw = distance travelled by screw in n rotations/n rotations

**21. How does negative error arise in the instrument?**

**Answer**

If the zero of the circular scale lies above the line of graduation then it is called negative zero error. When there is negative zero error, then the instrument reads less than the actual reading. Therefore in order to get the correct reading, the zero error should always be added from the observed reading.

**22. What is backlash error and how is it avoided? **

**Answer**

Due to constant use, there is space for the play of screw gauge but gradually this space increases with the use or wear and tear, so that when the screw is moved by rotating it in some direction, it slips in the nut and does not cover any linear distance for some rotation of the screw head. The error due to this is known as backlash error.

It is avoided by turning the screw always in the same direction.

**23. What is the difference between a nail and a screw?**

**Answer**

A screw are threaded to twist in, when turned with a screw driver while nails are smooth to slide in straight when pounded with hammer.

**24. How many types of motions does a screw have?**

**Answer**

Screw has two types of motions: linear and circular motions.

**25. What is the unit for least court of an instrument?**

**Answer**

Unit of Least count of an instrument is cm.

**26. Express micron in terms of meter.**

**Answer**

1 micron = 10^{-6} m.

**27. What is the principle of a physical balance?**

**Answer**

A physical balance works on the principle of moments. According to the principle of moments, under equilibrium condition, the clockwise moment due to the body on one side of beam equals the anti clockwise moment due to standard weights on the other side of beam.

**28. Express light year in terms of meter.**

**Answer**

1 light year = 9.46 × 10^{15 }m

**29. Plot a graph between square of time period (T ^{2}) and length (I) for a simple pendulum.**

**Answer**

Graph of T^{2} versus l for a simple pendulum

**30. Plot a graph between time period (T) and length (l) for a simple pendulum.**

**Answer**

Graph of T versus l for a simple pendulum

**31. Is oscillation same as vibration?**

**Answer**

Yes, the vibration is same as the oscillation.

**32. What is the relation between frequency (f) and time period (T)?**

**Answer**

The time period, T and frequency of oscillation, f are related as,

T = 1/T for f = 1/T

**33. What is ideal simple pendulum?**

**Answer**

An ideal pendulum is a simple pendulum consists a heavy mass (called the bob) considered as a point mass suspended by a thread which is considered to be mass less and inextensible or non-elastic, from a fixed point or rigid support and in which there is no friction between the support and the string.

**34. Does a wall clock run slow or fast in winter?**

**Answer**

Wall clock with a pendulum will run at a faster rate in winter as it pendulum rod get shorter and the pendulum will swing at a faster rate thus the clock would run faster in winters.

**35. Briefly, explain the need for measurements.**

**Answer**

Measurement is needed for precise description of any phenomenon happening in the world. For example, if a body is freely falling down to the ground, to understand this phenomenon we must know its velocity, time it will take to reach the ground etc. and to get answer to all our questions we need measurement.

**36. Distinguish between fundamental and derived units.**

**Answer**

Difference between fundamental units and derived units

**37. State the fundamental units of SI system. **

**Answer**

Fundamental units of SI system are:

**38. What is the importance of maintaining the standard units?**

**Answer**

The maintenance of standard units is essential because any variation in these standards would lead to wrong measurements, misleading results and confusing generalizations. The standards are preserved in such a way that they do not undergo any change with the change in temperature, pressure, humidity and other environmental changes.

**39. What are the main characteristics of a standard unit?**

**Answer**

Main characteristics of a standard unit are as follows

- It must be well defined.
- It must be of proper size. Very small or large size may cause inconvenience.
- It should be easily accessible
- It must be reproducible at all places without any difficulty.
- It must be accurately defined and must not change with time, place and physical conditions such as pressure, humidity, etc.
- It must be widely acceptable all over the world.

**40. What are fundamental units? Name some of the fundamental units.**

**Answer**

The units which can neither be derived from one another, nor can they be further resolved into other units are known as fundamental units. Some of the fundamental units are metre (length), kilogram (mass), second (time), Kelvin (temperature), ampere (current), etc.

**41. Consider the following cases where the zero of vernier scale and the zero of the main scale are clearly seen. If L.C. of the vernier calipers is 0.01 cm, write the zero error and zero correction in each case.**

**(a)**

**(b)**

**(c)**

**Answer**

**(a) Here, zero of the vernier scale coincides with the zero of the main scale,**

So, the zero error and zero error correction is nil,

(b) Here, zero of the vernier scale lies on the right of the zero of the main scale.

Also, 5^{th} vernier divisionis coinciding with some main scale division

Thus, zero error = 0 + 5 × L.C. = 0.05 cm

Hence zero correction = -0.05 cm

(c) Here, zero of the vernier scale lies on the left of the zero of the main scale.

Also, 5^{th} vernier division is coinciding with some main scale division

Thus, zero error = 0.5 × LC. = -0.05 cm

Hence zero correction =0.05 cm

**42. A screw gauge has 50 divisions on its circular scale and the pitch of the screw is 0.5 mm. What us its least count?**

**Answer**

Pitch of the screw = 0.5 mm

No of divisions on circular scale = 50

Least count = (pitch of the screw)/ (no. of divisions on the circular scale)

So, L.C. = 0.5/50

= 0.1 mm

**43. In case of a vernier calipers, 1 MSD = 1 mm. If 10 VSD coincide with 9 MSD; what is its least count?**

**Answer**

1MSD = 1mm

10 VSD = 9 mm

1 VSD = 9/10 mm

Least count = 1 MSD - 1 VSD

= 1/10 MSD

= 1/10 × 1 mm

= 0.1 mm

0.01 cm

**44. ****What is the zero error of a screw gauge?**

**Answer**

If the zero of the circular scale does not coincide with the zero of the main scale (pitch scale) when the end of the movable screw is brought in contact with the fixed end then the screw gauge is said to have a zero error.

**45. If the 4 ^{th} division of the circular scale coincides with the zero of the main scale of a screw gauge of least count 0.01 mm, what is its zero error?**

**Answer**

In this case, the zero error is positive

Least count of screw gauge = 0.01 mm

Thus, zero error = 0 + 4 × L.C. = 0.04mm

**46. If the 47 ^{th} division of the circular scale coincides with the zero of the main scale of a screw gauge of least count 0.01 mm and having 50 circular divisions, what is its zero error?**

**Answer**

In this case, the zero error is negative

Least count of screw gauge = 0.01 mm

Thus, zero error = (50 - 47) × L.C.

= 3 × 0.01

= 0.03 mm

**47. We can find the diameter of a wire by wrapping it around a pencil and measuring the length of tums with the help of a meter scale. Is this approach more accurate than determining the diameter of the wire with the help of a screw gauge?**

**Answer**

No, we cannot measure the diameter of a wire by wrapping it around a pencil because it is not very accurate. We can use screw gauge for this purpose as it can measure the diameter correct up to 1/100 of millimeter or even less.

**48. Fig. 2 shows the reading of a vernier calipers used for measuring the thickness of a metal sheet.**

**(i) Find the least count of the instrument.**

**(ii) Calculate the thickness of the metal sheet.**

**Answer**1MSD = 1mm

10 VSD = 9 mm

1VSD = 9/10 mm

Least count = 1 MSD - 1 VSD

= 1/10 MSD

= 1/10 × 1 mm

= 0.1 mm

= 0.01 cm

Thickness of the metal sheet

Main scale reading = 3.9 cm

Vernier scale division coinciding with main scale = 8

Vernier scale reading = 8 × 0.01 cm = 0.08 cm

Thickness of the metal sheet = 3.9 + 0.08 = 3.98 cm

**49. What is meant by pitch of a screw gauge? The pitch of a screw is 1 mm. Find the reading of the instrument shown in fig. 3.**

**Answer**When one complete rotation is given to the screw hand, it moves forward or backward by a distance is called pitch of the screw. It is distance between two consecutive threads of the screw.

Pitch of the screw = distance travelled by screw in n rotations/n rotations

Pitch of the screw = 1 mm

No of divisions on circular scale = 100

Least count = pitch/no of divisions =

= 0.01 mm

Main scale reading = 3 mm

Circular scale division coinciding with main scale = 42

Circular scale reading = 0.01 × 42 = 0.42

Final reading = 3 + 0.42 = 3.42 mm

**50. A screw thread has 20 threads in 1 cm and its circular scale has 50 divisions. Calculate its pitch and least count.**

**Answer**

Number of threads =20

Distance covered in 20 threads = 10 mm

Pitch of the screw gauge = 10/20 = 0.5 mm

No of divisions on circular scale = 50

Least count = pitch/no of divisions = 0.01 mm

**51. Define the following terms with reference to a simple pendulum:**

**(i) Oscillation**

**(ii) Time period**

**(iii) Frequency**

**(iv) Amplitude**

**Answer**

(i) Oscillation - One complete to and fro motion of a pendulum about its mean position is known as oscillation.

(ii) Time period - The time taken by a simple pendulum for an oscillation is known as the time period of a simple pendulum.

(iii) Frequency -the number of oscillation made by the pendulum in one second is called frequency. Its SI unit is Hertz (Hz).

(iv) Amplitude - Amplitude is the magnitude of the maximum deviation of the bob from the mean position on either side when an oscillation takes place.

**52. If a pendulum takes 0.5 s to travel from A to B as shown in fig. 4, find its time period and frequency.**

**Answer**Time period from A to B = 0.5s

For an ideal pendulum,

Time period from A to B = time period from B to C = time period from C to B = time period from

B to A

Total time period, T = time period from A to B + time period from B to C + time period from C to

B + time period from B to A

= 0.5 + 0.5 + 0.5 + 0.5

= 2 s

Frequency f = 1/T

= 1/2 = 0.5 Hz

**53. A piece of metal has a mass of 540 g and a volume of 200 cm ^{3}. Calculate the density of the metal in correct significant figures.**

**Answer**

Mass of the metal 540 g

Volume = 200 cm^{3}

Density = mass of metal/Volume

= 540/200

= 2.70 g/cm^{3}

**54. An alloy is made by mixing 540 g of copper of density 8 g cm ^{-3} with 240 g of iron of density 8 gcm^{-3}. Find the density of the alloy assuming that the volume of each metal does not change during mixing.**

**Answer**

Mass of copper = 540 g

Density of copper = 9 g/cm^{3}

Volume of copper used in the alloy = mass of copper/density

= 540/9

= 60 cm^{3}

Mass of iron = 240 g

Density of iron = 8 g/cm^{3}

Volume of iron used in the alloy = mass of iron/density

= 240/8

= 30 cm^{3}

Total mass of the alloy = 540 + 240 = 780 g

Total volume of the alloy = 60 + 30 = 90

Density of the alloy = mass of the alloy/density of the alloy = 780/90 = 8.67 g/cm^{3}

**55. The following diagrams (Fig. 5) show the use of a vernier calipers under three different situations. Study the diagrams carefully and note down the vernier readings in each case.**

**(a)**

**Measuring the diameter of rod**

**(b) **

**Measuring internal diameter of a cavity**

**(c)**

**Measuring depth of a cavity**

**Answer**

(a)

(b)

Measuring internal diameter of a cavity

(c)

Least count of vernier caliper = 0.01 cm

(i) Main scale reading = 5.5 cm

Vernier scale division coinciding with main scale = 6

Vernier scale reading = 6 × 0.01 cm = 0.06 cm

Diameter of rod = 5.5 + 0.06 = 5.56 cm

(i) Main scale reading = 1.6 cm

Vernier scale division coinciding with main scale = 5

Vernier scale reading = 5 × 0.01 cm = 0.05 cm

Internal diameter of a cavity = 1.6 + 0.05 = 1.65 cm

(iii) Main scale reading = 3.1 cm

Vernier scale division coinciding with main scale = 5

Vernier scale reading = 5 × 0.01 cm = 0.05 cm

Depth of a cavity = 3.1 + 0.05 = 3.15 cm

**56. What is meant by measurement? What are the fundamental units in SI system? Name them along with their symbols. What are the rules observed while writing the unit of a physical quantity?**

**Answer**

Measurement is an act or the result of comparison of a quantity whose magnitude is unknown with a predefined standard. Fundamental units in a SI system

(a) It must be of proper size. Very small or large size may cause inconvenience.

(b) It should be easily accessible

(c) It must be reproducible at all places without any difficulty.

(d) It must be accurately defined and must net change with time, place and physical conditions such as pressure, humidity, etc.

(e) It must be widely acceptable all over the world.

**57. Describe in steps, how would you use a vernier calipers to measure the length of a small rod?**

**Answer**

For measuring the length of an object using a vernier calipers, these steps are followed :-

(a) First of all we find the least count and zero error of the vernier calipers.

(b) Place the object whose length is to be measured below the lower jaws and move the jaw till it touches the object. Record the main reading.

(c) Note the division on the verier scale that coincides with some division of the main scale. Multiply this number of vernier division with least count. This is vernier scale reading.

(d) Record the observed length by adding the main scale reading and the vernier scale reading. Also, subtract zero error with its proper sign, if any, from the observed length to find the true length of the object.

**58. What is meant by zero error of a vernier calipers? How is it determined? Draw neat diagrams to explain it. How is it taken in account to get the correct measurement?**

**Answer**

(a) If the zero of the vernier scale lies to the right of the zero of main scale then it is called positive zero error.

(b) If the zero of the vernier scale lies to the left of the zero of main scale then it is called negative zero error

To determine the zero error, note the vernier division coinciding with any main scale division when two jaws are completely closed. Suppose n'" division is coinciding with main scale. Multiply this with the least count of vernier calliper.

Positive zero error = n×L.c.

Negative zero error = - (10 - n)×L.C.

To get the correct reading, the zero error is usually subtracted from the observed reading with its proper sign

Correct reading = observed reading - zero error

**59. Describe the procedure to measure the diameter of a wire with the help of a screw gauge.**

**Answer**

Following procedure is used to measure the diameter of a wire

- Calculate the least count and zero error of the screw gauge.
- Place the wire in between the studs. Turn the ratchet clockwise so as to hold the wire gently in between the studs. Record the main scale reading.
- Now record the division of circular scale that coincides with the base line of main scale. This circular scale division multiplied by least count will give circular scale reading.
- The observed diameter is obtained by adding the circular scale reading to the main scale reading. Subtract the zero error if any, with its proper sign, from the observed diameter to get the true diameter.

**60. Explain, how you would measure a length correctly with the help of a meter scale. Mention the precautions that you would observe. To what accuracy a meter scale can measure?**

**Answer**

In order to measure the length of an object using a metre rule, the metre rule must be placed with its marking close to the object, such that the zero marking on the scale coincides with one end of the object. Then the reading on the scale corresponding to the other end of the object will give the length of the object.

Precautions to be taken for measuring the length of the object, the eye must be kept vertically above the end of the object to avoid parallax and the corresponding marking along the line should be carefully read.

The meter scale can measure up to an accuracy of 1mm or 0.1. cm

**61. How will you record your observations while measuring the volume of an irregular solid by the displacement method using cylinder?**

**Answer**

- Fill the graduated cylinder with the water.
- Record the lower meniscus of water and let the value be V3.
- Tie the solid whose volume is to be measured to a strong string and lower it into the water gently.
- When the object is completely immersed in water, the level of water rises.
- Note the reading carefully and let the value be V
_{2} - Volume of the solid, V = V
_{2}– V_{1}

**62. How do you find the slope of a straight line obtained on a graph?**

**Answer**

(a) Take two points P and Q on the line, at a distance more than half the length of the line. The points should be so chosen that the value of x and y should be easily read on the axes.

(b) Draw horizontal and vertical lines from these points on the axes, and read the values of x, say x, and the value of y, say y1 for the point P. Similarly, the values of x, say x, and the value of y, say y_{2 }for the point Q.

(c) Calculate △y = y_{2} - y_{1} and △x = x_{1} - x_{2}. Calculate the slope of the graph m = △y/△x

**63. A graph plotted by taking T ^{2} on Y-axis and L on X-axis in an experiment of simple pendulum is a straight line. What relationship between T^{2 }and l, does this graph represent?**

**Answer**

Graph of T_{2} versus l of simple pendulum

The square of time period is directly proportional to the effective length of simple pendulum.

**64. How does the presentation of data in a tabular form help us in analyzing them? Explain with one example.**

**Answer**

The presentation of the data in a tabular form helps in quick grasping and analyzing the recorded observations. For example to measure a diameter using a vernier caliper we record the following data in a tabular form as follows

**65. Give a tabular format for recording the observations in an experiment of simple pendulum while measuring the time period of pendulum for its different lengths.**

**Answer**

Table to record time period of a simple pendulum for different effective lengths.

**66. Define the terms: (i) Oscillation, (ii) Amplitude, (iii) Frequency, and (iv) Time period, as related to a simple pendulum.**

**Answer**

(i) Oscillation - One complete to and fro motion of a pendulum about its mean position is known as oscillation.

(ii) Amplitude - Amplitude is the magnitude of the maximum deviation of the bob from the mean position on either side when an oscillation takes place.

(iii) Frequency - the number of oscillation made by the pendulum in one second is called frequency. Its SI unit is Hertz (Hz).

(iv) Time period - The time taken by a simple pendulum for an oscillation is known as the time period of a simple pendulum.

**67. Draw a neat diagram of a simple pendulum. Show on it the effective length of pendulum and one oscillation of pendulum.**

**Answer**

Diagram of simple pendulum

**68. What is simple pendulum? Name the factors on which the time period of a simple pendulum depends. Write the relation for the time period in terms of the above named factors.**

**Answer**

A simple pendulum consists a heavy point mass (called the bob) suspended by amass less and an inextensible or non-elastic thread from a fixed point or rigid support.

The time period of simple pendulum is directly proportional to the square root of the length of the pendulum

The time period of simple pendulum is inversely proportional to the square root of acceleration due to gravity

Where T is the time period,

L is length of the pendulum,

g is acceleration due to gravity

**69. Show how will you use physical balance to measure mass of an abject. Mention three precautions that you would observe. State two conditions for a beam balance to be true.**

**Answer**

To measure mass of a body using a physical balance

(i) Before starting, bring the plumb line just above the pointed projection by adjusting the leveling screws at the base. The beam is then gently raised using the lever. And it should be ensured that the pointer swings equally on both sides of the zero mark of the scale.

(ii) Now lower the beam gently and given body is kept on left pan.

(iii) Next, place some weight on the right pan form the weight box using the forceps.

(iv) Now the lever is turned towards right so that the beam rises and the power begins to swing to pointer swing on either side. It must be carefully noted that the side to which the pointer moves more, denotes lesser mass on that side.

(v) Go on adjusting the standard weights till the pointer swings equally on both sides of the zero mark.

(vi) At this stage, the total mass of weights on the right pan gives the mass of the body.

Three precautions to be taken to measure the mass of a body using beam balance are

(a) The beam must be gently lowered before adding or removing weights from the pan.

(b) The weights should not be carried with bare hands to avoid the change in weights due to moisture and dust particles from the surrounding

(c) Whenever you are near the actual weight, you should carefully try the weights in the descending order.

Conditions for a beam balance to be true are

(vii) Both the pans must be of equal weights.

(viii) Both the arms must be of equal lengths.

**70. In an experiment of simple pendulum, time for 20 oscillations of pendulum of a given length is measured and recorded as 40 s, 41 s, 42 s, 39 s and 38 s. Find the absolute error in each**

**Answer**

Time period of 20 oscillations of a simple pendulum are

Mean time period of pendulum = (40 + 41 + 42 + 39 + 38)/5

= 40 s

Absolute error △T_{1 }= 40 – 40 = 0

Absolute error △T_{2} = 40 – 41 = - 1

Absolute error △T_{1} = 40 – 42 = - 2

Absolute error △T_{3} = 40 – 39 = 1

Absolute error △T_{1 }= 40 – 38 = 2