The amount of work done to raise a mass '$m$' from the surface of the Earth to a height equal to the radius of the Earth '$R$' will be

Question

Accepted Answer

D. 1. **Recall the formula for gravitational potential energy.** The gravitational potential energy of a mass $m$ at distance $r$ from the centre of Earth (mass $M$) is
$$U = -\dfrac{GMm}{r}$$

2. **Write the initial and final potential energies.** At the surface, $r = R$, and at height $R$ above the surface, $r = R + R = 2R$, so
$$U_1 = -\dfrac{GMm}{R}, \quad U_2 = -\dfrac{GMm}{2R}$$

3. **Find the work done.** Since work done equals the change in potential energy,
$$W = U_2 - U_1 = -\dfrac{GMm}{2R} + \dfrac{GMm}{R} = \dfrac{GMm}{2R}$$
Using $g = \dfrac{GM}{R^2}$, this simplifies to
$$W = \dfrac{mgR}{2}$$

Hence, the answer is **D ($mg\dfrac{R}{2}$)**.

The amount of work done to raise a mass 'mmm' from the surface of the Earth to a height equal to the radius of the Earth 'RRR' will be

The amount of work done to raise a mass ' $m$ ' from the surface of the Earth to a height equal to the radius of the Earth ' $R$ ' will be