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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]

a
123gR
b
gR3
c
gR2
d
gR

detailed solution

Correct option is D

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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