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A tunnel is dug along the diameter of th...

A tunnel is dug along the diameter of the earth. The gravitational force on particle of mass m placed in the tunnel at a distance .x. from the centre .

Text Solution

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Mass of earth `M=4/3 piR^(3)rho`
Mass of imaginary sphere,
having radiu x,
`M^(1)=4/3pix^3rho("or")M^(1)/M=x^3/R^3`
`:.` Gravitational force on .m. due to `M_1`
`F=(GM^1m)/x^2("or") F=(Gm)/x^2(x^3/R^3M)=(GMmx)/R^3`
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