Escape velocity on the surface of earth is 11.2 km/s . Escape velocity from a planet whose mass is the same as that of earth and radius 1/4 that of earth is

Options

A. 2.8 km/s
B. 15.6km/s
C. 22.4 km/s
D. 44.8km/s

Answer

C

Explanation

At a certain velocity of projection the body will go out of the gravitational field of the earth and will never return to the earth, this velocity is known as escape velocity.
`v_(e)=sqrt((2GM_(e))/(R_(e)))`
Given `M_(e)=M_(p),R_(p)=(R_(e))/4`
`:.(v_(p))/(v_(e))=(M_(e))/(M_(e))xx(R_(e))/((R_(e))/4)=sqrt(4)=2`
`impliesv_(p)=2v_(e)=2xx11.2`
`=22.4km//s`