BITSAT2011PhysicsGravitationActual
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
Options
- A2 3 GMm R ²
- B0
- C1 3 GMm R ²
- D4 3 GMm R ²
Correct answer
A. 2 3 GMm R ²
Step-by-step solution
Change in force of gravity = GMm R ² - G M 3 ~m R ² (only due to mass M / 3 due to shell gravitational field is zero (inside the shell)) = 2 GMm 3 R ²