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A tunnel is dug along a chord of Earth h...

A tunnel is dug along a chord of Earth having length `sqrt(3R)` where R is radius of Earth. A small block is released in the tunnel from the surface of Earth. The particle comes to rest centre of tunnel. If the coefficient of friction between the block and the surface of tunnel is `mu=(2sqrt(3))/(n)`, then find n. Ignore the effect of rotation of Earth.

Text Solution

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`a_(x)=(GM)/(R^(3))(R//2)/(cosphi)cosphi=GM//(2R^(2))`
`V_(L)=-GM//R`
`V_(f)=-(GM)/(2R^(3))(3R^(2)-(R^(2))/(4))=-(GM)/(2R^(3))xx(11R^(2))/(4)=-(11GM)/(8R)`
`(sqrt(3)Rmu)/(2)(GM)/(2R^(2))=(3)/(8)(GM)/(R)`
`mu(sqrt(3))/(2)" "]`
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