First slide

Applications of SHM

Question

A freely falling body takes 2 seconds to reach the ground on a planet, when it is dropped from a height of 8m. If the period of a simple pendulum is π seconds on the planet. The length of a pendulum is (cm)

Moderate

A

100
B

50
C

25
D

200

Solution

$\begin{array}{rcl} e q u a t i o n o f m o t i o n f o r a f r e e l y f a l l i n g b o d y i s S & = & \frac{1}{2} {gt}^{2} \\ h e r e h= \frac{1}{2} {gt}^{2}, given h=8 \\ g i v e n 8 & = & \frac{1}{2} g_{p} {(2)}^{2} \\ \Rightarrow & g_{p} = 4 \\ t i m e p e r i o d o f s i m p l e p e n d u l u m T & = & 2π \sqrt{\frac{l}{g}} \\ g i v e n T & = & π=2π \sqrt{\frac{l}{4}} \\ l =1 m=100 cm. \end{array}$

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