Measurements And Experimentation - Questions & Answers

EXERCISE-1(A)

(A) MULTIPLE CHOICE TYPE :

1. The condition(s) essential for a unit to be accepted internationally :
(d) All of the above.

2. In mechanics, the three fundamental quantities are:
(a) Length, mass, time

3. How many units are fundamental and supplementary ?
(c) 7 fundamental, 2 supplementary

4. The fundamental unit is :
(d) Second

5. Which of the following unit is not a fundamental unit ?
(b) Litre

6. One astronomical unit is equal to :
(a) 1.496 × 10¹¹ metre

7. The distance of stars from earth in generally measured in :
(b) Light year

8. The unit of time is :
(c) leap year

9. 1 Å is equal to :
(a) 0.1 nm

10. One metric tonne is equal to:
(a) 10 quintal

11. One solar mass is equal to :
(b) 2 × 10³⁰ kg

12. One lunar cycle is nearly equal to :
(b) 29.5 days

13. One shake is equal to :
(b) 10^-8 s

14. Which of the following unit is equivalent to watt ?
(a) Volt × Ampere

15. Which one of the following is a derived unit ?
(c) Metre³

16. The S.I. unit of energy is :
(a) Joule

17. The S.I. unit of pressure is :
(b) Kg m^-1s^-2

18. Which of the following is the smallest unit ?
(c) Fermi

(B) VERY SHORT ANSWER TYPE :

1. What is meant by measurement ?
Measurement is the process of comparison of the given physical quantity with the known standard quantity of the same nature.

2. What do you understand by the term unit ?
Unit is the quantity of a constant magnitude which is used to measure the magnitudes of other quantities of the same nature.

3. How is a physical quantity expressed ?
Physical quantity = (numerical value) × (unit)

4. Name the three fundamental quantities.
Length, mass, and time.

5. What is the S.I. unit of Luminous intensity ?
candela (cd)

6. Define one parsec.
One parsec is the distance from where the semi major axis of orbit of earth (1 A.U.) subtends an angle of one second.

7. Define a fundamental unit.
A fundamental unit is that which is independent of any other unit or which can neither be changed nor can be related to any other fundamental unit.

8. Define a derived unit.
Derived units are those which depend on the fundamental units or which can be expressed in terms of the fundamental units.

9. Define standard metre.
One metre is the distance travelled by light in a vacuum in 1/299,792,458 of a second.

10. How is nanometre related to Angstrom ?
1 nm = 10 Å

11. Complete the following :
(a) 1 light year = 9.46 × 10¹⁵ m
(b) 1 m = 10¹⁰ Å
(c) 1 m = 10⁶ μ
(d) 1 micron = 10,000 Å
(e) 1 Fermi = 10^-15 m

12. Complete the following :
(a) 1 g = 10^-3 kg
(b) 1 mg = 10^-6 kg
(c) 1 quintal = 100 kg
(d) 1 a.m.u (or u) = 1.66 × 10^-27 kg

13. What is a leap year ?
A leap year is the year in which the month of February is of 29 days (i.e., 1 leap year = 366 days).

14. 'The year 2024 will have February of 29 days'. Is this statement true ?
Yes.

15. What is a lunar month ?
One lunar month is the time of one lunar cycle which is nearly 29.5 days.

16. Complete the following :
(a) 1 nano second = 10^-9 s
(b) 1 μs = 10^-6 s
(c) 1 mean solar day = 86400 s
(d) 1 year = 3.1536 × 10⁷ s

17. Name the physical quantities which are measured in the following units :
(a) u = mass
(b) ly = distance (or length)
(c) ns = time
(d) nm = length

18. Write the derived units of the following :
(a) speed = m s^-1
(b) force = kg m s^-2 (or N)
(c) work = kg m² s^-2 (or J)
(d) pressure = kg m^-1 s^-2 (or Pa)

19. How are the following derived units related to the fundamental units ?
(a) Newton = kg m s^-2
(b) Watt = kg m² s^-3
(c) Joule = kg m² s^-2
(d) Pascal = kg m^-1 s^-2

20. Name the physical quantities related to the following units :
(a) km² = area
(b) Newton = force
(c) Joule = energy (or work)
(d) Pascal = pressure
(e) Watt = power

(C) SHORT ANSWER TYPE :

1. What are the three requirements for selecting a unit of a physical quantity ?
(i) The unit should be of convenient size. (ii) It should be possible to define the unit without ambiguity. (iii) The unit should be reproducible.

2. What are the fundamental units in S.I. system ? Name them along with their symbols.
Length (metre, m), Mass (kilogram, kg), Time (second, s), Temperature (kelvin, K), Luminous intensity (candela, cd), Electric current (ampere, A), and Amount of substance (mole, mol).

3. Explain the meaning of derived unit with the help of one example.
Derived units are those which depend on the fundamental units or can be expressed in terms of the fundamental units. For example, the unit of area is metre × metre = (metre)², which is derived from the fundamental unit of length.

4. Name two units of length which are bigger than a metre. How are they related to the metre ?
Kilometre (km) and Astronomical unit (A.U.). 1 km = 1000 m; 1 A.U. = 1.496 × 10¹¹ m.

5. Name the three convenient units used to measure length ranging from very short to very long value. How are they related to the S.I. unit ?
Angstrom (Å) for very short length, Metre (m) for moderate length, and Light year (ly) for very long value. 1 Å = 10^-10 m; 1 ly = 9.46 × 10¹⁵ m.

6. Name the S.I. unit of mass and define it.
The S.I. unit of mass is kilogram (kg). In 1889, one kilogram was defined as the mass of a cylindrical piece of platinum-iridium alloy kept at International Bureau of Weights and Measures at Sevres near Paris.

7. State two units of mass smaller than a kilogram. How are they related to kilogram ?
Gram (g) and milligram (mg). 1 g = 10^-3 kg; 1 mg = 10^-6 kg.

8. State two units of mass bigger than a kilogram. Give their relationship with the kilogram.
Quintal and metric tonne. 1 quintal = 100 kg; 1 metric tonne = 1000 kg.

9. Name the S.I. unit of time and define it.
The S.I. unit of time is second (s). A second is defined as 1/86400th part of a mean solar day.

10. Name two units of time bigger than a second. How are they related to second ?
Minute (min) and hour (h). 1 min = 60 s; 1 h = 3600 s.

(D) NUMERICALS :

1. The wavelength of light of a particular colour is 5800 Å. Express it in (a) nanometre and (b) metre.
(a) 580 nm, (b) 5.8 × 10^-7 m

2. The size of a bacteria is 1 μ. Find the number of bacteria in 1 m length.
10⁶

3. The distance of a galaxy from the earth is 5.6 × 10²⁵ m. Assuming the speed of light to be 3 × 10⁸ m s^-1 find the time taken by light to travel this distance.
1.87 × 10¹⁷ s

4. The wavelength of light is 589 nm. What is its wavelength in Å ?
5890 Å

5. The distance of the nearest star, Proxima Centauri, from the Earth is 4.0 × 10¹³ km. Express it in light year.
4.2 light year

6. It takes time 8 min for light to reach from the sun to the earth surface. If speed of light is taken to be 3 × 10⁸ m s^-1, find the distance from the sun to the earth in km.
1.44 × 10⁸ km

7. 'The distance of a star from the earth is 8.33 light minutes.' What do you mean by this statement ? Express the distance in metre.
It means light takes 8.33 minutes to travel from the star to the Earth. Distance = 1.5 × 10¹¹ m.

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EXERCISE-1(B)

(A) MULTIPLE CHOICE TYPE :

1. The strip of a vernier callipers is used to measure :
(b) Depth of a beaker

2. On bringing the two jaws of a vernier callipers together, the 6th division of vernier scale coincides with the main scale. If the least count of the vernier callipers is 0.01 cm, then its zero error is :
(a) + 0.06 cm

3. A microscope has its main scale with 20 divisions in 1 cm and vernier scale with 25 divisions, the length of which is equal to the length of 24 divisions of main scale. The least count of microscope is :
(a) 0.002 cm

4. Identify the correct use of the thimble of a screw gauge :
(d) To mark circular scale.

5. The circular head of a screw gauge is divided into 50 divisions and the screw moves 1 mm ahead in two revolutions of the circular head. Its pitch would be :
(a) 0.5 mm

6. Identify the incorrect statement from the following:
(d) Vernier callipers has a higher precision with a larger least count whereas screw gauge has a lower precision with a smaller least count.

(B) VERY SHORT ANSWER TYPE :

1. Define the least count of an instrument.
The least count of an instrument is the smallest measurement that can be taken accurately with it.

2. How can you decrease the least count of a vernier callipers ?
The least count of a vernier callipers can be decreased by (i) increasing the number of divisions on the vernier scale and (ii) decreasing the value of one division on main scale.

3. Define the term 'Vernier constant'.
The least count of vernier is equal to the difference between the values of one main scale division and one vernier scale division. It is also called the vernier constant.

4. When is a vernier callipers said to be free from zero error ?
When the movable jaw is brought in contact with the fixed jaw, and the zero mark of the vernier scale coincides perfectly with the zero mark of the main scale, it is said to be free from zero error.

5. Name the part of the vernier callipers which is used to measure the following :
(a) external diameter of a tube, outside jaws
(b) internal diameter of a mug, inside jaws
(c) depth of a small bottle, strip
(d) thickness of a pencil. outside jaws

6. State the difference between positive and negative zero error of a vernier callipers.
If the zero mark of the vernier scale is to the right of the main scale zero mark, the zero error is positive. If it is to the left of the main scale zero mark, the zero error is negative.

7. Define the pitch of a screw gauge.
The pitch of a screw is the distance moved along its axis by the screw in one complete rotation of its head.

8. State one use of a screw gauge.
It is used to measure the diameter of a wire or thickness of a paper up to an accuracy of 0.001 cm.

9. State the purpose of ratchet in a screw gauge.
The ratchet helps in holding the given object gently between the stud and the flat end of the screw without applying excessive pressure.

10. State the difference between positive and negative zero error of a screw gauge.
If the zero mark of the circular scale is below the base line of the main scale, the zero error is positive. If it is above the base line, it is negative.

11. Name the instrument which can measure accurately the following :
(a) the diameter of a needle, screw gauge
(b) the thickness of a paper, screw gauge
(c) the internal diameter of the neck of a water bottle, vernier callipers
(d) the diameter of a pencil. vernier callipers

12. Which of the following measures a small length to a high accuracy : metre rule, vernier callipers, screw gauge ?
screw gauge

13. Name the instrument which has the least count:
(a) 0.1 mm = vernier callipers
(b) 1 mm = metre rule
(c) 0.01 mm = screw gauge

(C) SHORT ANSWER TYPE :

1. Explain the meaning of the term 'least count of an instrument' by taking a suitable example.
The least count is the smallest measurement that can be accurately taken with an instrument. For example, a metre rule has graduations at every 1 mm, so its least count is 1 mm.

2. A boy makes a ruler with graduations in cm on it (i.e., 100 divisions in 1 m). To what accuracy this ruler can measure ? How can this accuracy be increased ?
The ruler can measure with an accuracy of 1 cm. The accuracy can be increased by making smaller divisions on the ruler, such as 10 divisions per cm (i.e., mm graduations).

3. A boy measures the length of a pencil and expresses it to be 2.6 cm. What is the accuracy of his measurement ? Can he write it as 2.60 cm ?
The accuracy of his measurement is 0.1 cm. No, he cannot write it as 2.60 cm because that implies an accuracy of 0.01 cm which his instrument does not provide.

4. Define least count of a vernier callipers. How do you determine it ?
Least count of vernier callipers is the difference between the values of one main scale division and one vernier scale division. It is determined by dividing the value of one main scale division by the total number of divisions on the vernier scale.

5. A vernier callipers has a zero error + 0.06 cm. Draw a neat labelled diagram to represent it.
(Diagram cannot be drawn, but it represents the zero mark of the vernier scale lying to the right of the main scale zero, with the 6th vernier division coinciding with a main scale division.)

6. State three uses of a vernier callipers.
It is used to measure (i) the length of a rod, (ii) internal and external diameters of a hollow cylinder, and (iii) the depth of a small beaker.

7. Name the two scales of a vernier callipers and explain, how it is used to measure a length correct up to 0.01 cm.
The two scales are the main scale and the vernier scale. By observing which vernier scale division perfectly aligns with a main scale division, fractional parts of the main scale division can be accurately read, reducing the least count to 0.01 cm.

8. Explain the terms (i) pitch, and (ii) least count of a screw gauge. How are they determined ?
(i) Pitch is the linear distance moved by the screw along its axis in one complete rotation. (ii) Least count is the distance moved by the screw when rotated by one division on the circular scale. It is determined by Pitch / Total number of divisions on circular scale.

9. How can the least count of a screw gauge be decreased ?
By decreasing the pitch or by increasing the total number of divisions on the circular scale.

10. What do you mean by zero error of a screw gauge ? How is it accounted for ?
Zero error occurs if the zero mark of the circular scale does not coincide with the base line of the main scale when the flat ends touch. The correct reading is obtained by subtracting the zero error (with its proper sign) from the observed reading.

11. A screw gauge has a least count 0.001 cm and zero error + 0.007 cm. Draw a neat diagram to represent it.
(Diagram cannot be drawn, but it represents the zero mark of the circular scale 7 divisions below the base line of the main scale when the studs touch.)

12. What is backlash error ? Why is it caused ? How is it avoided ?
Backlash error occurs when reversing the direction of rotation, the screw remains stationary for a part of the rotation. It is caused by wear and tear of threads. It is avoided by turning the screw continuously in one direction only.

(D) LONG ANSWER TYPE :

1. What is meant by zero error of a vernier callipers ? How is it determined ? Draw neat diagrams to explain it. How is it taken in account to get the correct measurement ?
Zero error is a mechanical error where the zero mark of the vernier scale does not coincide with the zero of the main scale when jaws are in contact. It is determined by finding the vernier division that coincides with a main scale division and multiplying it by the least count. Correct reading = observed reading - zero error (with sign).

2. Draw a neat labelled diagram of a vernier callipers. Name its main parts and state their functions.
Parts: Outside jaws (for external measurements), Inside jaws (for internal measurements), Strip (for depth), Main scale (reads up to 1 mm), Vernier scale (reads up to 0.1 mm).

3. Describe in steps, how would you use a vernier callipers to measure the length of a small rod ?
(i) Find the least count and zero error. (ii) Place the rod between the outside jaws. (iii) Note the main scale reading. (iv) Note the coinciding vernier division and multiply by least count. (v) Add to main scale reading to get observed length. (vi) Subtract zero error with sign to get true length.

4. Draw a neat and labelled diagram of a screw gauge. Name its main parts and state their functions.
Parts: Ratchet (advances screw gently), Sleeve (marks main scale and base line), Thimble (marks circular scale), Main scale (reads length up to 1 mm), Circular scale (reads length up to 0.01 mm).

5. Describe the procedure to measure the diameter of a wire with the help of a screw gauge.
(i) Find the least count and zero error. (ii) Place the wire gently between the stud and flat end using the ratchet. (iii) Note main scale reading. (iv) Note coinciding circular scale division and multiply by least count. (v) Add to main scale reading for observed diameter. (vi) Subtract zero error with sign to get true diameter.

(E) NUMERICALS :

1. A stop watch has 10 divisions graduated between the 0 and 5 s marks. What is its least count ?
0.5 s

2. A vernier has 10 divisions and they are equal to 9 divisions of main scale in length. If the main scale is calibrated in mm, what is its least count ?
0.01 cm

3. A microsope is provided with a main scale graduated with 20 divisions in 1 cm and a vernier scale with 50 divisions on it of length same as of 49 divisions of main scale. Find the least count of the microscope.
0.001 cm

4. A boy uses a vernier callipers to measure the thickness of his pencil. He measures it to be 1.4 mm. If the zero error of vernier callipers is + 0.02 cm, what is the correct thickness of pencil ?
1.2 mm

5. A vernier callipers has its main scale graduated in mm and 10 divisions on its vernier scale are equal in length to 9 mm. When the two jaws are in contact, the zero of vernier scale is ahead of zero of main scale and 3rd division of vernier scale coincides with a main scale division. Find : (i) the least count and (ii) the zero error of the vernier callipers.
(i) 0.01 cm (ii) + 0.03 cm

6. The main scale of a vernier callipers is calibrated in mm and 19 divisions of main scale are equal in length to 20 divisions of vernier scale. In measuring the diameter of a cylinder by this instrument, the main scale reads 35 divisions and the 4th division of vernier scale coincides with a main scale division. Find : (i) least count and (ii) radius of cylinder.
(i) 0.005 cm, (ii) 1.76 cm

7. In a vernier callipers, there are 10 divisions on the vernier scale and 1 cm on the main scale is divided in 10 parts. While measuring a length, the zero of the vernier lies just ahead of 1.8 cm mark and 4th division of vernier coincides with a main scale division. (a) Find the length. (b) If zero error of vernier callipers is -0.02 cm, what is the correct length ?
(a) 1.84 cm, (b) 1.86 cm

8. Vernier scale readings are as shown in the figures given below. Give the actual reading provided : (a) the instrument has a zero error of +0.02 cm. (b) the instrument has a zero error of -0.03 cm.
(a) 1.04 cm, (b) 1.07 cm

9. While measuring the length of a rod with a vernier callipers, Fig. 1.14 below shows the position of its scales. What is the length of the rod ?
3.36 cm

10. 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 ?
0.005 mm or 0.0005 cm

11. The thimble of a screw gauge has 50 divisions. The spindle advances 1 mm when the screw is turned through two revolutions. (i) What is the pitch of the screw gauge ? (ii) What is the least count of the screw gauge ?
(i) 0.5 mm (ii) 0.01 mm

12. The pitch of a screw gauge is 1 mm and its circular scale has 100 divisions. In measurement of the diameter of a wire, the main scale reads 2 mm and 45th mark on circular scale coincides with the base line. Find : (i) the least count, and (ii) the diameter of the wire.
(i) 0.001 cm (ii) 0.245 cm

13. When a screw gauge of least count 0.01 mm is used to measure the diameter of a wire, the reading on the sleeve is found to be 1 mm and the reading on the thimble is found to be 27 divisions. (i) What is the diameter of the wire in cm ? (ii) If the zero error is + 0.005 cm, what is the correct diameter ?
(i) 0.127 cm (ii) 0.122 cm

14. A screw gauge has 50 divisions on its circular scale and its screw moves by 1 mm on turning it by two rotations. When the flat end of the screw is in contact with the stud, the zero of circular scale lies below the base line and 4th division of circular scale is in line with the base line. Find : (i) the pitch, (ii) the least count and (iii) the zero error, of the screw gauge.
(i) 0.5 mm (ii) 0.01 mm (iii) + 0.04 mm

15. Two micrometers are shown in figures given below. Give the actual reading shown provided : (a) The least count of the instrument = 0.001 cm and zero error = +0.05 mm. (b) The least count of the instrument = 0.001 cm and zero error = -0.021 cm.
(a) 0.316 cm (b) 0.667 cm

16. Fig. 1.15 below shows the reading obtained while measuring the diameter of a wire with a screw gauge. The screw advances by 1 division on main scale when circular head is rotated once. Find : (i) pitch of the screw gauge, (ii) least count of the screw gauge, and (iii) the diameter of the wire.
(i) 1 mm (ii) 0.02 mm (iii) 4.94 mm

17. 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 up to 0.001 mm with its help ?
500

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EXERCISE-1(C)

(A) MULTIPLE CHOICE TYPE :

1. The pendulum used in a clock is :
(b) Compound pendulum

2. The effective length of a pendulum is related with time period as :
(c) T² ∝ l

3. A simple pendulum is made by suspending a bob of mass 1 kg by a string of length l. Now if the length of this pendulum is increased to 4l, then its time period T will :
(b) become twice

4. The time period of a seconds' pendulum clock is :
(b) 2 s

5. Time period of a simple pendulum is given by :
(b) T = 2π√(l/g)

6. The time period of a simple pendulum depends on:
(a) Length of the pendulum

7. The time period of two pendulums of length 1 m and 16 m are in the ratio :
(b) 1 : 4

8. The length of a simple pendulum is made one-fourth. Its time period becomes :
(d) half.

9. The length of a seconds' pendulum is nearly :
(c) 1.0 m

10. Identify the incorrect statement(s) from the following :
(d) (I), (II) and (III)

(B) VERY SHORT ANSWER TYPE :

1. Define 'amplitude of oscillation'.
The maximum displacement of the bob from its mean position on either side, is called the amplitude of oscillation.

2. Define the terms : (i) oscillation (ii) amplitude (iii) frequency, and (iv) time period as related to a simple pendulum.
(i) Oscillation: One complete to and fro motion of the bob. (ii) Amplitude: The maximum displacement of the bob from its mean position. (iii) Frequency: The number of oscillations made in one second. (iv) Time period: The time taken to complete one oscillation.

3. Name two factors on which the time period of a simple pendulum does not depend.
The mass of the bob and the amplitude of oscillation.

4. How is the time period of a simple pendulum affected, if at all, in the following situations : (a) the length is made four times, (b) the acceleration due to gravity is reduced to one-fourth.
(a) The time period is doubled. (b) The time period is doubled.

5. How are the time period T and frequency f of an oscillation of a simple pendulum related ?
f = 1/T

6. Two simple pendulums A and B have equal lengths, but their bobs weigh 50 gf and 100 gf respectively. What would be the ratio of their time periods ? Give reason for your answer.
1 : 1. Reason: Time period does not depend on the weight (or mass) of the bob.

7. What is a seconds' pendulum ?
A pendulum with a time period of oscillation equal to two seconds is known as a seconds' pendulum.

8. State the numerical value of the frequency of oscillation of a seconds' pendulum. Does it depend on the amplitude of oscillation ?
0.5 s^-1. No.

(C) SHORT ANSWER TYPE :

1. What is a simple pendulum ? Is the pendulum used in a pendulum clock simple pendulum ? Give reason to your answer.
A simple pendulum is a heavy point mass suspended from a rigid support by a massless and inextensible string. No, the pendulum used in a pendulum clock is a compound pendulum because it is a rigid body capable of oscillating about a horizontal axis, not a point mass.

2. Draw a neat diagram of a simple pendulum. Show on it the effective length of the pendulum and its one oscillation.
(Diagram cannot be drawn, but shows rigid support, string, bob, effective length from support to center of bob, and one complete to and fro path from mean position.)

3. Name two 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.
Effective length (l) and acceleration due to gravity (g). Relation: T = 2π√(l/g).

4. How do you measure the time period of a given pendulum ? Why do you note the time for more than one oscillation ?
The time (t) for 20 complete oscillations is measured with a stopwatch, and time period T is calculated as t/20. Time for more than one oscillation is noted to minimize errors due to the least count of the stopwatch and human reaction time.

5. Two simple pendulums A and B have lengths 1.0 m and 4.0 m respectively at a certain place. Which pendulum will make more oscillations in 1 minute ? Explain your answer.
Pendulum A will make more oscillations. Since T ∝ √l, the time period of A is half that of B. A shorter time period means a higher frequency, so A makes more oscillations.

6. State how does the time period of a simple pendulum depend on (a) length of pendulum, (b) mass of bob, (c) amplitude of oscillation and (d) acceleration due to gravity.
(a) Directly proportional to the square root of its effective length. (b) Does not depend on the mass of bob. (c) Does not depend on the amplitude of oscillation. (d) Inversely proportional to the square root of acceleration due to gravity.

(D) LONG ANSWER TYPE :

1. How does the time period (T) of a simple pendulum depend on its length (l) ? Draw a graph showing the variation of T² with l. How will you use this graph to determine the value of g (acceleration due to gravity) ?
The square of time period (T²) is directly proportional to the effective length (l). The graph of T² vs l is a straight line passing through the origin. Since T²/l = 4π²/g, the value of g can be determined by using g = 4π² / (Slope of T² vs l graph).

(E) NUMERICALS :

1. A simple pendulum completes 40 oscillations in one minute. Find its (a) frequency, (b) time period.
(a) 0.67 s^-1 (b) 1.5 s

2. The time period of a simple pendulum is 2 s. What is its frequency ? What name is given to such a pendulum ?
0.5 s^-1, seconds' pendulum

3. A seconds' pendulum is taken to a place where acceleration due to gravity falls to one-fourth. How is the time period of the pendulum affected, if at all ? Give reason. What will be its new time period ?
The time period increases (it is doubled) because T ∝ 1/√g. Its new time period will be 4 s.

4. Find the length of a seconds' pendulum at a place where g = 10 m s^-2 (Take π = 3.14).
1.0142 m

5. Compare the time periods of two pendulums of length 1 m and 9 m.
1 : 3

6. A pendulum completes 2 oscillations in 5 s. (a) What is its time period ? (b) If g = 9.8 m s^-2, find its length.
(a) 2.5 s, (b) 1.55 m

7. The time periods of two simple pendulums at a place are in the ratio 2 : 1. What will be the ratio of their lengths ?
4 : 1

8. It takes 0.2 s for a pendulum bob to move from mean position to one end. What is the time period of pendulum ?
0.8 s

9. How much time does the bob of a seconds' pendulum take to move from one extreme of its oscillation to the other extreme ?
1 s

Competency Focussed Questions

(F) ASSERTION - REASON TYPE QUESTIONS :

(i) Assertion (A) : The unit used to measure speed is an example of a derived unit. Reason (R) : Derived units can neither be changed nor can be related to any other fundamental unit.
(d) Assertion is false but reason is true

(ii) Assertion (A) : Smaller the least count of an instrument, more precise the measurement made by using it. Reason (R) : Least count of an instrument is the smallest measurement that can be taken accurately with it.
(a) Both A and R are true and R is the correct explanation of A

(iii) Assertion (A) : The least count of a screw gauge can be decreased by increasing the pitch and decreasing the total number of divisions on circular scale. Reason (R) : Least count of screw gauge is directly proportional to pitch of the screw gauge.
(c) Assertion is true but reason is false

(iv) Assertion (A) : A pendulum clock goes slow (i.e. the time period of oscillation increases) when it is taken to mines. Reason (R) : This is due to increase in the value of acceleration due to gravity g.
(d) Assertion is false but reason is true

(G) CASE STUDY BASED QUESTIONS :

1. During a Physics practical, Ayush and Reema measured the length of a metal rod using two measuring instruments A and B. Ayush used instrument A and obtained a reading of 25.4 cm, while Reema used instrument B and obtained a reading of 25.36 cm.
(a) Why did Ayush and Reema get different values for the same length ?
They used measuring instruments with different least counts (different precisions).

(b) Which measuring instrument is more accurate, A or B ?
Instrument B is more accurate because it measures up to two decimal places (smaller least count).

(c) Can you identify the measuring instruments A and B ?
Instrument A could be a metre rule (least count 0.1 cm) and instrument B could be a vernier callipers (least count 0.01 cm).

(d) Why is it important to use S.I. units while recording measurements ?
It ensures measurements are universally accepted and understood without ambiguity.

2. A student performs an experiment to study the dependence of the time period (T) of a simple pendulum on its length. The length of the pendulum is changed each time. For every length, the time taken for 20 oscillations is recorded. The recorded observations are as follows:
(a) Calculate the time period for each length of the pendulum.
For l=0.40m, T=1.27 s; For l=0.60m, T=1.55 s; For l=0.90m, T=1.90 s; For l=1.00m, T=2.01 s.

(b) Draw a graph between T² and the length of the pendulum.
(A straight line graph passing through the origin is plotted with T² on the y-axis and length l on the x-axis.)

(c) What conclusion can be drawn from the graph ?
The square of the time period (T²) is directly proportional to the length (l) of the pendulum.

(d) Which physical parameter can be calculated using the slope of the above graph ?
The acceleration due to gravity (g).

(e) If the same experiment is conducted on the Moon, would the graph remain the same ? Give reason.
No. The slope of the T² vs l graph is inversely proportional to acceleration due to gravity (g). Since g on the Moon is less than on Earth, the slope of the graph will be steeper.