The escape velocity from the earth's surface is v. The escape velocity from the surface of another planet having a radius, four times that of earth and same mass density is

Options

A. `2v_e`
B. `3v_e`
C. `4v_e`
D. `v_e`

Answer

C

Explanation

`v_e=sqrt((3gS)/2)`
`v_e=sqrt((2G4/3piR^3p)/R)=Rsqrt(8/3piGp)`
`v_epropR`
`(v_e)/(v_p)=(R_e)/(R_p)rArr(v_e)/(v_p)=R/(4R)`
`v_p=4v_e`