Q.

At what depth below the surface of the earth, acceleration due to gravity g will be half its  value 1600 km above the surface of the earth

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a

4.2×106 m

b

3.19×106 m

c

1.59×106 m

d

None of these

answer is A.

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Detailed Solution

Radius of earth R = 6400 km ∴h=R4Acceleration due to gravity at a height hgh=gRR+h2=gRR+R42=1625gAt depth 'd' value of acceleration due to gravity gd=12gh       (According to problem)⇒gd=121625g⇒g1−dR=121625gBy solving we get d=4.3×106m
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