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Q.

A narrow tunnel is dug along a diameter of earth. A small object is released at one end of the tunnel. If g be the acceleration due to gravity on the surface of earth and R be the radius of earth, then velocity of the object when it reaches the centre of earth is 

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a

gR2

b

12gR

c

3gR4

d

gR

answer is C.

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Detailed Solution

Inside of earth g'=g.rR, where r is the radial distance of the point where acceleration due to gravity is g'.

Since g' is varying linearly with r, its average value is, g¯=0+g2=12g

∴v2=0+2.g¯.R=2.g2.R⇒v=gR

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