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12.Kinetic Theory of Gases
normal
Which of the following plots represents schematically the dependence of the time period of a pendulum, if measured and plotted as a function of the amplitude of its oscillations? (Note amplitude need not be small)
A

B

C

D

(KVPY-2017)
Solution

$(a)$ Time period of a simple pendulum depends on its amplitude as,
$T=2 \pi \sqrt{\frac{l}{g}} \cdot\left(1+\frac{\theta_{0}^{2}}{16}\right)$
where, $\theta _{0}=$ angular a mplitude from mean position. Clearly, $T$ increases with $\theta$ and its relation is parabolic. Its variation is as shown below in the figgure.
Standard 11
Physics