The escape velocity of a body from the surface of the earth is expressed in terms of density and diameter of the earth, it is found that it is

Options

A. directly proportional to the mass of the body
B. directly proportional to the diameter of the earth
C. inversely proportional to the diameter of the earth
D. inversely proportional to the density of the earth

Answer

B

Explanation

For the escapvelocity of a body from the surface of the earth is
`v_(e)=sqrt((2GM)/(R ))=sqrt(2G.(4)/(3)(pi R^(3)rho)/(R ))`
`= sqrt((4R^(2).(2piG rho))/(3))=2R sqrt((2pi G rho)/(3))`
`therefore v_(e)prop 2R` or the diameter of the earth.