A planet has the radius twice that of earth and has same density as that of earth. If `V_(p)andV_(e)` are the escape velocities for the planet and earth, then which of the following correct relation is:

Options

A. `V_(p)=V_(e)`
B. `V_(e)=2V_(p)`
C. `V_(p)=2V_(e)`
D. `V_(p)=sqrt(2)V_(e)`

Answer

C

Explanation

`V_(e)=sqrt((2GM)/(R))=sqrt((2G((4)/(3)piR^(3))rho)/(R))`
`=Rsqrt((8)/(3)piGrho)`
`VpropR`
`(V_e)/(V_p)=(R_e)/(R_p)=(R_e)/(2R_e)" "[becauseR_(p)=2R_(e)]`
`=(1)/(2)`
`thereforeV_(p)=2V_(e)`