Tow spherical planet A and B have same mass but of acceleartion due to gravity at the surface of A to its value at surface of B is

Options

A. `1:4`
B. `1:2`
C. `4:1`
D. `8:1`

Answer

C

Explanation

Mass of two planets is same so
`4/3 pi R_(1)^(3)p_(1)=4/3piR_(2)^(3)p_(2)`
or `(R_(1))/(R_(2))=(P_(2))/(P_(1))^(1//3)=(1/8)^(1//3)=1/2`
`(g^(1))/(g_(2))=(GM//R_(1)^(2))/(GM//R_(2)^(2))=(R_(2))/(R_(1))^(2)=(2)^(2)=4`