First slide

Simple hormonic motion

Question

A simple pendulum of length 1m is taken to height R (radius of the earth) from the earth’s surface. The time period of small oscillation of the pendulum at that point is

Moderate

A

2 s
B

3 s
C

4 s
D

1 s

Solution

$v a l u e o f g a t a h e i g h t h \frac{g R^{2}}{{(R + h)}^{2}} h e e r e h = R a n d g b e c o m e s \frac{g}{4} t i m e p e r i o d o f o s c i l l a t i o n o f a p e n d u l u m T = 2 π \sqrt{\frac{l}{g}} o r i g i n a l t i m e p e r i o d 2 s e c a n d i f g d e c r e a s e s t o \frac{g}{4 t i m e p e r i o d i n c r e a s e t o t w o t i m e s} i . e, i t w i l l b e 4 s e c$

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