There are two planets. The ratio of radius of the two planets is K, but ratio of acceleration due to gravity of both planets is g. What will be the ratio of their escape velocity?

Options

A. `(Kg)^(1//2)`
B. `(Kg)^(2)`
C. `(Kg)^(-1//2)`
D. `(Kg)^(-2)`.

Answer

A

Explanation

Given `(g_(1))/(g_(2))=g and (R_(1))/(R_(2))=K`
Since escape velocity `v=sqrt(2gR)`
`therefore (v_(1))/(v_(2))=sqrt((g_(1))/(g_(2)).(R_(1))/(R_(1)))=sqrt(gK)=(Kg)^(1//2)`
Thus correct choice is (a).