The escape velocity of an object from the earth depends upon the mass of the earth ( M ), its mean density `(rho)`, its radius ( R ) and the gravitational constant ( G ). Thus the formula for escape velocity is

Options

A. `v_c = R sqrt((8pi)/(3) G rho)`
B. `v_e = M ((8pi)/(3) GR)`
C. `v_e = sqrt(2GMR)`
D. `v_e =sqrt( (2GM)/(R^2))`

Answer

A

Explanation

Escape velocity `v_e = sqrt( (2GM)/(R )) = sqrt((2G)/( R) 4/3 pi R^3 rho) `
` = sqrt( (8pi)/(3) G rho R^2) = R sqrt( (8pi)/(3) G rho)`