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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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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 |
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Level 1: 80%+
NEET - 2018
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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 |
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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 |
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A simple pendulum has a time period \(T\) in air. The bob is then completely immersed and continues to oscillate freely in a non-viscous liquid whose density is \(\left ( \dfrac{1}{16}\right )^\mathrm{th} \) of that of the bob. Assuming no damping and only the effect of buoyancy, what is the new time period of oscillation?

1. \( 2 T \sqrt{\dfrac{1}{14}} \) 2. \( 2 T \sqrt{\dfrac{1}{10}} \)
3. \(4 T \sqrt{\dfrac{1}{15}} \) 4. \( 4 T \sqrt{\dfrac{1}{14}} \)
Subtopic:  Angular SHM |
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A simple pendulum is vibrating in an evacuated chamber. It will oscillate with:
1. constant amplitude 2. decreasing amplitude
3. increasing amplitude 4. none of these
Subtopic:  Angular SHM |
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The motion of a simple pendulum executing simple harmonic motion is represented by the equation;
\({y}={A} \sin (\pi {t}+\phi),\) where time is measured in seconds. The length of the pendulum is:
1. \(97.23~\text{cm}\) 
2. \(25.3~\text{cm}\) 
3. \(99.4~\text{cm}\) 
4. \(406.1~\text{cm}\) 
Subtopic:  Angular SHM |
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JEE
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What is the ratio of the frequency of a simple pendulum on the Earth to that of an identical pendulum on the Moon, given that the acceleration due to gravity on the Moon is six times weaker than on the Earth?
1. \(36:1\)
2. \(6:1\)
3. \(\sqrt6:1\)
4. \(1:1\)
Subtopic:  Angular SHM |
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For a simple pendulum, the graph between \(T^2\) and \(L\) is:
1. a straight line passing through the origin
2. parabola
3. circle
4. ellipse
Subtopic:  Angular SHM |
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A simple pendulum has some time period \(T\). What will be the percentage change in its time period if its amplitude is decreased by \(5\%\)\(?\)
1. \(6\)\(\%\)
2. \(3\%\)
3. \(1.5\%\)
4. it will remain unchanged
Subtopic:  Angular SHM |
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