Escape velocity from a planet is `v_(e)`. If its mass is increased to 16 times and its radius is increased to 4 times, then the new escape velocity would be

Options

A. `v_(e)`
B. `sqrt(2)v_(e)`
C. `2v_(e)`
D. `2 sqrt(2)v_(e)`

Answer

C

Explanation

Escape velocity of a body on earth surface is given by
`v_(e)=sqrt((2GM)/(R))`
where, G is gravitational constant, M is mass of planet and `R_(e)` is radius
where `M'=16M,R'=4R`
then, `v'_(e)=sqrt((2G(16M))/((4R)))=2sqrt((2GM)/(R))rArr v'_(e)=2v_(e)`.