Question

A man of mass m starts falling towards a planet of mass M and radius R. As he reaches near to the surface, height realizes that he will pass through a small hole in the planet. As he enters the hole, he seen that the planet is realize made of two pieces a spherical shell of negligible thickness of mass $\frac{2M}{3}$ and a point mass $\frac{M}{3}$ at the centre. Change in the force of gravity experienced by the man is?

• A. $\frac{2}{3}\frac{GMm}{R^2}$
• B. $0$
• C. $\frac{1}{3}\frac{GMm}{R^2}$
• D. $\frac{4}{3}\frac{GMm}{R^2}$

Answer 1

The correct option is C $\frac{1}{3}\frac{GMm}{R^2}$

Gravitational force on the mass when falling towards the planet was $\frac{{GM}_m}{R^2}$ $G$ here is constant. $M$ is mass of white planet is $\frac{m}{3}+\frac{2m}{3}$ $m$ is the mass of the mass and $r$ is radius of planet once $h$ has entered whole in the planet the force he was experiencing earlier due to outer small of the planet becomes zero now he experiences force due to point mass at center force equal to $\frac{{GM}_m}{{3R}^2}$ thus change in force is initial final force experienced is $\frac{{GM}_m}{{3R}^2}$.