Question

A body of mass $m$ is approaching towards the centre of a hypothetical hollow planet of mass $M$ and radius $R$. The speed of the body when it passes the centre of the planet through a diametrical tunnel is:

• A. $\frac{GM}{R}$
• B. $\sqrt{\frac{2GM}{R}}$
• C. Zero
• D. none of these

Answer 1

The correct option is B $\sqrt{\frac{2GM}{R}}$

potential energy at a surface is given by $\frac{GMm}{R}$,

and potential energy at the center of the hollow sphere is 0.

the total energy of the system will be conserved so $K.E{.}_1+P.E{.}_1=K.E{.}_2+P.E{.}_2$

$0+\frac{GMm}{R}=\frac{1}{2}m{v}^2+0$

$v=\sqrt{\frac{2GM}{R}}$.

so the best possible option is D.