Question

work done in lifting a body from the surface of the earth to a height h against the gravitational force is (h=r)​

Answer 1

Given :

Height of body (h) = R

To find :

Work done = ?

Solution :

• Work done = change in  energy
• Initial potential energy = mgR

• At height the value of g increases,

      g¹ = g/(1+h/R)

         = g/(1+1)

         = g/2

• Final potential energy = mg¹h = mgR/2

• Work done = mgR - mgR/2

                   = mgR/2

Work done is mgR/2 J

Answer 2

The work done in lifting a body from the surface of the earth is (mgr)/2

Explanation:

The work done is product of force and displacement which is change in energy.

In lifting a move from the surface of earth, the potential energy acts on the body.

The change in potential energy is given by the formula:

ΔU = (mgh)/(1 + h/r)

h = r (given in question)

Now, the ΔU becomes,

ΔU = (mgr)/(1 + 1)

∴ ΔU = (mgr)/2