Question

a body of mass M is situated at a height h from the surface of Earth if the gravitational is acting on the body derive an expression for potential energy of the body

Answer 1

Few assumptions,

Mass of earth = M

Universal gravitation constant = G

Radius of earth = R

So assuming in the initial state, body of mass ‘m’ is at the surface of earth

P.E1=−(G∗M∗m)/RP.E1=−(G∗M∗m)/R

When body is move to a height ‘h’

P.E2=−(G∗M∗m)/(R+h)P.E2=−(G∗M∗m)/(R+h)

(-ve sign is because there is attraction force)

So change in potential energy is

= P.E2 - P.E1

=−(G∗M∗m)/(R+h)+(G∗M∗m)/R=−(G∗M∗m)/(R+h)+(G∗M∗m)/R

=(G∗M∗m)(1/R)−(1/(R+R))Sinceh=R=(G∗M∗m)(1/R)−(1/(R+R))Sinceh=R

=(G∗M∗m)/(2∗R)

Answer 2

Potential energy = Mass × gravitational × Height
P.E. = Mgh
Hope it helps