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Question

Let ω be the angular velocity of the earth's rotation about its axis. Assume due to gravity on the earth's surface has the same value at the equator and the poles. An object weighed at the equator gives the same reading as a reading taken at a depth a below earth's surface at a pole(d<<R). The value of d is:

A
ω2R2g
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B
ω2R22g
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C
2ω2R2g
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D
Rgg
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Solution

The correct option is A ω2R2g
Lets ω= the angular velocity of the earth's rotation about it's axis.

g= acceleration due to gravity.

R= radius of earth

d= depth a below earth surface at which the acceleration due to gravity is same at the equator and the poles.

geff due to rotation =geff due to depth

gω2R=g(1dR)

gRω2=ggdR

Rω2=gdR

d=ω2R2g

The correct option is A.

1452099_1210690_ans_8f2bbaa0d72b4ae6889ea2035790acb7.png

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