if a body is raised through height H on the surface of earth and the energy is e then for the same amount of energy the body on the surface of moon will rise through the height of

Dear Student,

​​​​As per your query the solution is stated below- ​​​
Given -
Mass= m kg
Height =h m
Acceleration due to gravity=g m/s2
Acceleration due to gravity at height H is given by :
Now,
g¹=g(1-2h/R)

Loss of weight =ΔW=mg-mg¹
=m[g-g¹]
=m[g-g(1-2h/R)]
=mg[1-(1-2h/R)]
=mg[1-1+2h/R]
=mg x 2h/R
=2mgh/R, which is the required solution.

Regards