Excercise 1(C)
:
Very Short Answer Type Questions with Answers
1. Define amplitude of oscillation.
Ans: Amplitude is the maximum displacement of the bob from its mean (rest) position.
2. Define the terms:
(i) Oscillation — One complete to-and-fro motion of the pendulum is called one oscillation.
(ii) Amplitude — The maximum distance the bob moves on either side of the mean position.
(iii) Frequency — The number of oscillations per 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.
Ans:
(i) Mass of the bob
(ii) Amplitude of oscillation (for small amplitudes)
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
Ans: Time period becomes twice (T ∝ √L).
(b) The acceleration due to gravity is reduced to one-fourth
Ans: Time period becomes twice (T ∝ 1/√g).
5. How are the time period (T) and frequency (f) of an oscillation of a simple pendulum related?
Ans: T = 1/f or 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.
Ans: The ratio is 1:1.
Reason: Time period is independent of the mass of the bob.
7. What is a seconds' pendulum?
Ans: A seconds' pendulum is a pendulum with a time period of 2 seconds (1 second for each swing).
8. State the numerical value of the frequency of oscillation of a seconds' pendulum. Does it depend on the amplitude of oscillation?
Ans: Frequency = 0.5 Hz.
No, it does not depend on amplitude (for small amplitudes).
— Short Answer Type
Question 1
What is a simple pendulum? Is the pendulum used in a pendulum clock simple pendulum? Give reason to your answer.
Answer
A simple pendulum is a heavy point mass (known as bob) suspended from a rigid support by a massless and inextensible string.
No, the pendulum used in the pendulum clock is not a simple pendulum, but it is a compound pendulum.(i.e., a body capable of oscillating about a horizontal axis passing through it.)
Question 2
Draw a neat diagram of a simple pendulum. Show on it the effective length of the pendulum and its one oscillation.
Answer
Below diagram shows the effective length and one oscillation of a simple pendulum:
Question 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.
Answer
Factors affecting the time period of a simple pendulum are —
1. Effective length of the pendulum — the time period of oscillation is directly proportional to the square root of its effective length.
i.e., T∝√L
2. Acceleration due to gravity — the time period of oscillations is inversely proportional to the square root of acceleration due to gravity
i.e., T∝ √g
Relation between time period, effective length and acceleration due to gravity is as follows —
T=2Ï€√l/g
where,
T = Time period
l = effective length of the pendulum
g = acceleration due to gravity.
Question 4
How do you measure the time period of a given pendulum? Why do you note the time for more than one oscillation ?
Answer
To measure the time period of a given pendulum, we record the time for 20 or more oscillations and then divide the recorded time with the number of oscillations. Hence, we get the time period for one oscillation.
The time for more than one oscillation is noted, as the least count of stop watch is either 1s or 0.5s. It cannot record the time period in fraction such as 1.2s or 1.4s and so on.
Hence, it is made possible by noting the time t for 20 oscillations or more and then dividing it by the number of oscillations.
Question 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.
Answer
Given,
lA = 1.0m
lB = 4.0m
Since,
T∝√l
∴,
TA/TB=√lA/ √lB
Substituting the values of l in the formula above we get,
So,
TA / TB =√1/4
i.e., TA: TB = 1 : 2
∴, time period of B is more (twice) than that of A. Hence, A will make more oscillations (twice) in a given time than B.
Question 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.
Answer
The time period of a simple pendulum varies as follows —
(a) Length of pendulum (l) — Time period of a simple pendulum is directly proportional to the square root of the length of the pendulum.
T∝√L
(b) Mass of bob — Time period of a simple pendulum is independent of the mass of the bob.
(c) Amplitude of oscillation — Time period of a simple pendulum is independent of the amplitude of oscillation
(d) Acceleration due to gravity (g) — Time period of a simple pendulum is inversely proportional to the the square root of acceleration due to gravity .
T∝√g
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