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Question

A simple pendulum has a time period T1 when on the earth's surface and T2 when taken to a height R above the earth's surface, where R is the radius of the earth. The value of T2T1 is

A
1
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B
2
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C
4
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D
2
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Solution

The correct option is D 2
The time period of a simple pendulum depends upon the acceleration due to gravity

T=2πLg

Assuming L is constant, then

T1g .....(1)

Acceleration due to gravity at a height h above the surface of the earth is given as

gh=g(1+hR)2

at h=R

gh=g(1+RR)2=g4 .....(2)

From eq. (1),

T2T1=g1g2=ggh

Now using eq.(3)

T2T1=gg/4=2

Hence, option (d) is correct.

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