A man of mass m starts falling towards a planet of mass M and...

A man of mass m starts falling towards a planet of mass

\mathrm{M}

and radius

\mathrm{R}

. As he reaches near to the surface, he realizes that he will pass through a small hole in the planet. As he enters the hole, he sees that the planet is really made of two pieces a spherical shell of negligible thickness of mass

2 \mathrm{M} / 3

and a point mass

\mathrm{M} / 3

at the centre. Change in the force of gravity experienced by the man is

Options

A $\frac{2}{3} \frac{\mathrm{GMm}}{\mathrm{R}^{2}}$
B0
C $\frac{1}{3} \frac{\mathrm{GMm}}{\mathrm{R}^{2}}$
D $\frac{4}{3} \frac{\mathrm{GMm}}{\mathrm{R}^{2}}$

Correct answer

A. $\frac{2}{3} \frac{\mathrm{GMm}}{\mathrm{R}^{2}}$

Step-by-step solution

\quad

Change in force of gravity =

\frac{\mathrm{GMm}}{\mathrm{R}^{2}}-\frac{\mathrm{G} \frac{\mathrm{M}}{3} \mathrm{ m}}{\mathrm{R}^{2}} (only due to mass \mathrm{M} / 3

due to shell gravitational field is zero (inside the shell)) =

\frac{2 \mathrm{GMm}}{3 \mathrm{R}^{2}}

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