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In the above question, if the soild sphe...

In the above question, if the soild sphere is a large rock, what is the gravitational acceleration at a point on the surface of the rock at a point just above the cavity ?

A

`(GM)/(R^(2))`

B

`(GM)/(2R^(2))`

C

`(GM)/(8R^(2))`

D

`(7GM)/(8R^(2))`

Text Solution

Verified by Experts

The correct Answer is:
B
Gravitational acceleration due to soild sphere at a point on the surface of sphere, `g = (GM)/(R^(2))`.
Gravitational acceleration at a point on the surface of sphere of radius `(R//2)` which is to be evacuated
is `g' = (G(M//8))/((R//2)^(2)) = (GM)/(2R^(2))`
`:.` Gravitational acceleration at a point just outside the sphere when cavity is created
`= g - g' = (GM)/(R^(2)) - (GM)/(2R^(2)) = (GM)/(2R^(2))`
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