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Question

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

A
GMemR3er
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B
GMemR2e
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C
GMemR2er5
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D
2GMemR3er
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Solution

## The correct option is A GMemR3erGiven, Mass of the Earth=Me, Radius of the Earth=Re Gravitational field inside a solid sphere of mass M and radius R at a distance a from its centre is given by, E=GMaR3Since, the particle of mass m is inside the Earth at distance r, so the gravitational field on the particle due the Earth will be, Ee=GMerR3e So, the force on the particle of mass m will be, F=mEe=GmMerR3e Hence, option (a) is the correct answer. Key Concept: The gravitational field inside a solid sphere of radius R and mass M at distance r is given by E=GMrR3

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