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. `100km//sec`
B. `50km//sec`
C. `200km//sec`
D. `25km//sec`

Answer

A

Explanation

In first case, `v_(e)=sqrt((2GM)/R)` or `50=sqrt((2GM)/R)`
second case, `v'_(e)=[(2G(4M)^(2))/R]^(1//2) =2sqrt((2GM)/R)`
`=2xx50=100km//sec`