A man of mass m starts falling towards a planet of mass M and radius R. As he reaches near to the surface realizes that he will pass through a small hole in the planet. As he enters the hole he seen that the planet really made of two places a spherical shell of negligible thickness of mass `(2M)/(3)` and a point mass `(M)/(3)` of centre. Change in the force of gravity experienced by the man is

Options

A. `(2)/(3)(GM)/(R^(2))`
B. `0`
C. `(1)/(3)(GMm)/(R^(2))`
D. `(4)/(3)(GMm)/(R^(2))`

Answer

A

Explanation

Gravitational field inside the shell is zero, but the force on the man due to the point mass at the centre is
`F_("new")=(GMm)/(3R^(2)),F_("old")=(GMm)/(R^(2))`
Change in force `=(2GMm)/(3R^(2))` ltbr.