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

Question

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 $2 M /3$ and a point mass $M /3$ at the centre. Change in the force of gravity experienced by the man is

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Answer:

A

Solution:

Change in force of gravity $= \frac{GMm}{R ^{2}} - \frac{G \frac{M}{3} m}{R ^{2}}$ (only due to mass $M /3$ due to shell gravitational field is zero (inside the shell)) $= \frac{2 GMm}{3 R ^{2}}$

TestHub · Accepted Answer

Change in force of gravity = R 2 GMm ​ − R 2 G 3 M ​ m ​ (only due to mass M /3 due to shell gravitational field is zero (inside the shell)) = 3 R 2 2 GMm ​

Physics - Gravitation Question with Solution | TestHub

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