Q94 / 125 · BITSAT 2011 · Physics
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
- Correct answerA$\frac{2}{3} \frac{\mathrm{GMm}}{\mathrm{R}^{2}}$
- B0
- C$\frac{1}{3} \frac{\mathrm{GMm}}{\mathrm{R}^{2}}$
- D$\frac{4}{3} \frac{\mathrm{GMm}}{\mathrm{R}^{2}}$
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))
$$
=\frac{2 \mathrm{GMm}}{3 \mathrm{R}^{2}}
$$
Hence, the correct answer is option: 'A'.