For a planet having mass equal to mass of the earth and radius is one fourth of radius of the earth. Then which one of the following statements is correct?

Options

A. The escape velocity for this planet will be 11.2 km/sec
B. The escape velocity for this planet will be 5.6 km/sec
C. The escape velocity for this planet will be 22.4 km/sec
D. The escape velocity for this planet will be 44.8 km/sec

Answer

C

Explanation

Escpae velocity `v_(c)=sqrt((2GM)/(R))=11.2km//sec`
If M = M and `R=(R)/(4)` then
`v_(c)=sqrt((2GM)/(R/4))=sqrt((8GM)/(R))`
`=2sqrt((2GM)/(R))`
`=2xx11.2=22.4km//sec`