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Q.

A tunnel is dug along a diameter of the earth. If Me and R. 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

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a

GMemRe3r

b

GMemRe3r

c

GMemRe3r

d

GMemRe2r

answer is A.

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Detailed Solution

Let us first calculate the mass of the inner solid sphere of radius r, Mass of the inner solid sphere isM′=Me43πRe3×43πr3=r3MeRe3 Now, g=GMer3Re3×1r2 or g=GMerRe3Force on the particle of mass m=mg=GMemrRe3
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A tunnel is dug along a diameter of the earth. If Me and R. 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