A mass m on the surface of the Earth is shifted to a target equal to the radius of the Earth. If R is the radius and M is the mass of the Earth, then work done in this process is

Options

A. `(mgR)/2`
B. mgR
C. 2 mgR
D. `(mgR)/4`

Answer

A

Explanation

`U_(E)=(-GMm)/R`
`U_(T)=(-GMm)/(2R)`
`W=U_(T)-U_(E)=(-GMm)/(2R)+(GMm)/R`
= `(GMm)/(2R)=(gR^(2)m)/(2R)=(mgR)/2`