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Question

# A tunnel is dug along a diameter of the earth. If Me and Re are the mass and radius, respectively, of the earth, then the force on a particle of mass m placed in the tunnel at a distance r from the centre is :

A
GMemR3er
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B
GMemR3er
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C
GMemR3er
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D
GMemR2er
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Solution

## The correct option is A GMemR3erLet us first calculate the mass of inner solid sphere of radius r.Mass of inner sphere M′=Me43πRe3×43πr3=MeRe3r3Now,g=GMer3Re3×1r2or g=GMerRe3Force on particle of mass m=mg=GMemrRe3 Note that those layers of the sphere which have radii larger than r do not have any contribution to the gravitational force.

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