Energy required in moving a body of mass `m` from a distance 2R to 3R from centre of earth of mass M is

Options

A. GMm/6R
B. `GMm//12R^(2)`
C. `GMm//8R`
D. `GMm//3R^(2)`

Answer

A

Explanation

P.E. of the body at a distance 2R from the centre of the earth `=-(GMm)/(2R)`
and P.E. of the same body at a distance 3r from the centre of the earth `=-(GMm)/(3R)`
`therefore` Increase in P.E. = Work done = Energy required
`=(-(GMm)/(3R))-(-(GMm)/(2R))`
`=(GMm)/(2R)-(GMm)/(3R)=(GMm)/(6R)`