Q. 113.7( 3 Votes )

A tunnel is dug along a diameter if the earth. Find the force on a particle of mass m placed in the tunnel at a distance x from the center.

Answer :

Let the mass of the earth be . Here, we have to find the gravitational field inside a solid sphere. The particle is placed at a distance x from the center. Now, the part outside the sphere of radius x, will have no influence on it as the electric field inside a spherical shell is zero. Hence, only the mass up to x will contribute to the electric field.


The density is uniform. Therefore, mass of the sphere would then be




Now the gravitational force on the particle at a distance x is




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