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 ( in centi meter)

Moderate

A

100
B

50
C

25
D

200

Solution

$A f r e e l y f a l l i n g b o d y, u = 0, t h e n h e i g h t h f r o m w h e r e b o d y i s d r o p p e d i s h= \frac{1}{2} {gt}^{2}, given h=8, g is acceleration due to gravity 8 = \frac{1}{2} g_{p} {(2)}^{2}, g_{p} is acceleration due to gravity o n p l a n e t \Rightarrow g_{p} = 4, s u b s t i t u t e i n t i m e p e r i o d o f s i m p l e p e n d u l u m T = 2π \sqrt{\frac{l}{g_{p}}}, given Time period T=π π=2π \sqrt{\frac{l}{4}} \Rightarrow l =1 m=100 centi meter.$

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