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The acceleration due to gravity g and me...

The acceleration due to gravity g and mean density of the earth `rho` are related by which of the following relations ? (Where G is the gravitational constant and R is the radius of the earth .)

A

`rho=(3g)/(4pi GR )`

B

`rho=(3g)/(4pi GR^(3))`

C

`rho=(4pi gR^(2))/(3G)`

D

`rho=(4 pi gR^(3))/(3G)`

Text Solution

Verified by Experts

The correct Answer is:
A
Acceleration due to gravity (g)`=Gxx(M)/(R^(2))`
`G((4//3)piR^(3)xxrho)/(R^(2))=Gxx(4)/(3)piRxxrho" or rho=(3g)/(4pi GR)`
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