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At what depth below the surface of the e...

At what depth below the surface of the earth, the value of g is the same as that at a height of 5km?

A

1.25km

B

2.5 km

C

5 km

D

10 km

Text Solution

Verified by Experts

The correct Answer is:
D
Acceleration due to gravity at the surface of earth
`g_h=g(1+h/R)^-2`
`g_h=g (g-(2h)/R)`
Acceleration due to gravity at depth d from the surface of the earth
`g_d= g(1-d/R)`
Given: `g_h=g_d`
`therefore (2h)/R=d/R`
or d=2h
or d=10 km
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