If the radius of a planet is R and its density is `rho` , the escape velocity from its surface will be

Options

A. `v_(e) prop R sqrt(rho)`
B. `v_(e) prop (1)/(sqrt(rhoR))`
C. `V_(e) prop rhoR`
D. `V_(e) prop (sqrt(rho))/( R)`

Answer

A

Explanation

`v_(e)=sqrt((2GM)/(R ))=sqrt((2G.(4)/(3)pi R^(3)rho)/(R ))`
`= sqrt((8)/(3)G pi rho R^(2))=2R sqrt((2)/(3)G pi rho)`
Thus `v_(e) prop R sqrt(rho)`
`because` The remaining quantities are constant.