JEE Main · PhysicsHard
A thin uniform spherical shell of mass and radius is placed in a region of space. A particle of mass is released from rest at a distance from the center of the shell. The time taken by the particle to reach the surface of the shell is given by . If the shell were replaced by a point mass at the center, the time taken to reach the same distance would be . Find the ratio .
- A.
- B.
- C.
- D.
Show correct answer & step-by-step solution
Correct answer: A —
Solution
- For a particle outside a shell or point mass, the gravitational potential is .
- The time taken to fall from to depends only on the potential difference and the field in the region .
- Since the field for is identical for both the shell and the point mass, the motion is identical until the surface is reached.
- Hence the answer is (A).
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