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Q.

A narrow tunnel is dug along a diameter of earth. A body is released at one end of the tunnel. It R be the radius of earth then the velocity of the body when it passes through the centre of earth is [g= Acceleration due to gravity at the surface]

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a

123gR

b

gR3

c

gR2

d

gR

answer is D.

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Detailed Solution

At a radial distance r(r≤R), acceleration due to gravity g'=grR∴ Average acceleration of the body a=gRR+02=g2∴ V2=0+2.a.R⇒V2=2.g2R⇒V=gR
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