A man of mass $m$ starts falling towards a planet of mass $M$ and radius 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 $2 M / 2$ and a point mass $M / 3$ at the centre. Change in the force of gravity experienced by the man is

\frac{2}{3} \frac{G M m}{R^{2}}

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\frac{1}{3} \frac{G M m}{R^{2}}

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\frac{4}{3} \frac{G M m}{R^{2}}

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Solution

The correct option is A $\frac{2}{3} \frac{G M m}{R^{2}}$
Gravitational force exerted by a spherical shell inside it is zero.
Therefore, the change in force of gravity experienced by the man while entering the shell is the force exerted by the shell when he is outside the shell, which is $\frac{2 G M m}{3 R^{2}}$

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Q. 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{2 M}{3}

and a point mass

\frac{M}{3}

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

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The correct option is A 23GMmR2Gravitational force exerted by a spherical shell inside it is zero.Therefore, the change in force of gravity experienced by the man while entering the shell is the force exerted by the shell when he is outside the shell, which is 2GMm3R2