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Question

A tunnel is dug along the diameter of the earth and a body is released from rest into the tunnel. Find the speed of the body at the center of the tunnel.

A
7.3 km/sec
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B
7.9 km/sec
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C
8.4 km/sec
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D
9.2 km/sec
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Solution

The correct option is B 7.9 km/sec
Initial gravitation potential,
Vi=GMR
Final gravitation potential,
Vf=3GM2R
Change in gravitational potential energy,
ΔE=m ΔV
=m(VfVi)=3GMm2R+GMmR
=GMm2R
Loss in potential energy = Gain in Kinetic energy
GM m 2R=12 mv2
v=GMR=2GM2R=11.21.414
v=7.9 km/sec

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