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Q. No.
What is the time period of a simple pendulum with a length of \(1~\text{m},\) if the acceleration due to gravity at its location is \(\pi^2~\text{m}\text{s}^{-2} \text{?}\)
1. \(1~\text{s}\) 2. \(2~\text{s}\)
3. \(3~\text{s}\) 4. \(4~\text{s}\)
Subtopic:  Angular SHM |
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Level 1: 80%+
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Given below are two statements: 
Assertion (A): If the length of a simple pendulum increases by \(4\text{%},\) the percentage change in the time period is \(2\text{%}.\)
Reason (R): The time period of a simple pendulum is directly proportional to the square root of its length.
  
1. Both (A) and (R) are True and (R) is the correct explanation of (A).
2. Both (A) and (R) are True but (R) is not the correct explanation of (A).
3. (A) is True but (R) is False.
4. Both (A) and (R) are False.
Subtopic:  Angular SHM |
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If the length of a pendulum is made 9 times and mass of the bob is made 4 times , then the value of time period becomes

(1) 3T

(2) 3/2T

(3) 4T

(4) 2T

Subtopic:  Angular SHM |
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Level 1: 80%+
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For a simple pendulum, a graph is plotted between its kinetic energy (\(KE\)) and potential energy (\(PE\)) against its displacement \(d\). Which one of the following represents these correctly? (graphs are schematic and not drawn to scale)

1. 2.
3.   4.
Subtopic:  Angular SHM |
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Level 1: 80%+
JEE
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A pendulum is hung from the roof of a sufficiently high building and is moving freely to and fro like a simple harmonic oscillator. The acceleration of the bob of the pendulum is \(20\text{ m/s}^2\) at a distance of \(5\text{ m}\) from the mean position. The time period of oscillation is:
1. \(2\pi \text{ s}\)
2. \(\pi \text{ s}\)
3. \(2 \text{ s}\)
4. \(1 \text{ s}\)

Subtopic:  Angular SHM |
 86%
Level 1: 80%+
NEET - 2018
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A pendulum has time period T. If it is taken on to another planet having acceleration due to gravity half and mass 9 times that of the earth then its time period on the other planet will be

(1) T

(2) T

(3) T1/3

(4) 2T

Subtopic:  Angular SHM |
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Level 1: 80%+
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A pendulum oscillates about its mean position \(\mathrm{C}.\) The position where the speed of the bob becomes maximum is: (ignore all dissipative forces)

                  

1. \(\mathrm{A}\) 2. \(\mathrm{B}\)
3. \(\mathrm{C}\) 4. \(\mathrm{D}\)
Subtopic:  Angular SHM |
 85%
Level 1: 80%+
Hints
Given below are two statements: 
Assertion (A): If a pendulum is suspended in a lift and the lift is falling freely, then its time period becomes infinite.
Reason (R): The free-falling body has acceleration equal to the acceleration due to gravity.
 
1. Both (A) and (R) are True and (R) is the correct explanation of (A).
2. Both (A) and (R) are True but (R) is not the correct explanation of (A).
3. (A) is True but (R) is False.
4. Both (A) and (R) are False.
Subtopic:  Angular SHM |
 83%
Level 1: 80%+
Hints

In a simple pendulum, the period of oscillation T is related to length of the pendulum l as

(1) lT=constant

(2) l2T=constant

(3) lT2=constant

(4) l2T2=constant

Subtopic:  Angular SHM |
 83%
Level 1: 80%+
Hints
Which of the following graphs best represents the relation between the square of the time period and the length of a simple pendulum?
1. 2.
3. 4.
Subtopic:  Angular SHM |
 82%
Level 1: 80%+
JEE
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