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

Answer

A

Explanation

Let us first calculate the mass of inner solid sphere of radius `r`.
Mass of inner solid sphere, `M'`
`=(M_(e))/(4/3piR_(e)^(3))xx4/3pir^(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 a particle of mass `m=mg=(GM_(e)r)/(R_(e)^(3))`