The work done in lifting a body of mass ‘m’ from the earth’s surface, through a height ‘h’ is mg R/3 where ‘g’ is the acceleration due to gravity on the earth’s surface and ‘R’ is the radius of the earth. Calculate the value of h.

If the height h is comparable to the radius R of the earth, the expression for work done in lifting the body through height h is:

W = m g R [1 + (h/R)]

So that m g R / 3 = m g R [1 + (h/R)]

⇒ h = R / 2

^R/₃ = ^h/_{(1 + h/a)}

⇒ ^{(R + h)}/₃ = h

⇒ R = 2h

∴ h = ^R/₂