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A solid sphere of mass M and radius R is...


A solid sphere of mass M and radius R is surrounded by a spherical shell of same mass and radius 2R as shown. A small particle of mass m is relased from rest from a height h`(lt lt R)` above the shell. There is a hole in the shell.
Q. What time will it take to move from A to B?

A

`=(4R^(2))/(sqrt(GMR))`

B

`gt(4R^(2))/(sqrt(GMR))`

C

`lt(4R^(2))/(sqrt(GMR))`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
Given that `(h lt lt R)` so the velocity at A is also zero
we can see here that the acceleration always increases from 2 R to R its value must be greater than
`a=(GM)/(4R^(2))` (at A) `thereforetlt(v)/(a)impliestltsqrt((GM)/(R))xx(4R^(2))/(GM)impliestlt(4R^(2))/(sqrt(GMR))`
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