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 km/s
B. 50 km/s
C. 200 km/s
D. 25 km/s

Answer

A

Explanation

In first case , `v_e = sqrt((2GM)/( R) ) = 50`
In second case , `v._e = [ (2G (4M) )/( R) ]^(1//2) = 2 sqrt((2GM)/( R)) = 2 xx 50 = 100 km//s`