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

Options

A. `(GM_(e)m)/(R_(e)^(3))`
B. `(GM_(e)m)/(R_(e)^(3)r)`
C. `(GMmR_(e)^(3))/r`
D. `(GMm)/(R_(e)^(2))`

Answer

A

Explanation

Let us of first calculate the mass of the inner solid sphere of radius `r`.
Mass of the inner solid sphere is
`M'=(M_(e))/(4/3piR_(e)^(3))xx4/3=pir^(2)=(M_(e))/(R_(e)^(3)r^(3))`
Now `g=(GM_(e)r^(3))/(R_(e)^(3))xx1/(r^(2))` or `g=(GM_(e)r)/(R_(e)^(3))`
Force on the particle of mass `m=mg=(GM_(e)mr)/(R_(e)^(3))`