Q. 125.0( 1 Vote )

A tunnel is dug along a chord of the earth at a perpendicular distance R/2 from the earth’s center. The well of the tunnel may be assumed to be frictionless. Find the force exerted by the wall on a particle of mass m when it is at a distance x from the center of the tunnel.

Answer :

Let the mass of Earth be . Here, , and .

Now, the force exerted by the wall on the particle is perpendicular to the tunnel. This force will be balanced by the gravitational force exerted by the sphere of radius r. The component of force perpendicular to the tunnel is given by .



Therefore,


Here, and Force due to the sphere of radius r is


Therefore,



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