The total amount of work that must be done on a body of mass m so that it escapes from the gravitational influence of a planet of radius R and mass M is given by

Options

A. `(GMm)/( R)`
B. `(2GMm)/( R)`
C. `(3GMm)/(2R)`
D. `(3GMm)/(R^(2))`

Answer

A

Explanation

Work done = Energy imparted to the body
`=(1)/(2)mv_(e)^(2)=(1)/(2)m[(2GM)/(R )]=(GMm)/(R )`