The escape velocity corresponding to a planet of mass `M` and radius `R` is `50 km s^(-1)`. If the planet's mass and radius were `4M` and `R`, respectively, then the corresponding escape velocity would be

Options

A. `100 kms^(-1)`
B. `50 kms^(-1)`
C. `200 kms^(-1)`
D. `25kms^(-1)`

Answer

A

Explanation

In the first case `v_(e)=sqrt((2GM)/R` or `50= sqrt((2GM)/R)`
In the second case `v_(3)=[(2G(4M)^2)/R]^(1/2)=2sqrt((2GM)/R)`
`=2xx50=100kms^(-1)`