Question

A tunnel is dug along the diameter of the earth. There is particle of mass `m` at the centre of the tunnel. Find the minimum velocity given to the particle so that is just reaches to the surface of the earth. `(R =` radius of earth)
A. `sqrt((GM)/R)`
B. `sqrt((GM)/(2R))`
C. `sqrt((2GM)/R)`
D. it will reach will the help of a negligible velocity.

Answer 1

Correct Answer - A
Let the minimum speed imparted to the particle of mass `m` so that it just reaches the surface of the earth is `v`. Applying the principle of conservation of energy.
`1/2mv^(2)+(-3/2(GM)/Rm)=(GM)/Rm+0`
Solving we get `v=sqrt((GM)/R)`