1. Given data

• Mass of object: $m = 1\,\text{kg}$
• Acceleration due to gravity at earth's surface: $g = 10\,\text{m s}^{-2}$
• Radius of earth: $R = 6400\,\text{km} = 6.4 \times 10^6\,\text{m}$
• Height above surface: $h = 3R$

So the final distance from the center of earth is $r_f = R + h = R + 3R = 4R.$

2. Potential energy formula

Gravitational potential energy at distance $r$ from earth's center is $U = -\frac{GMm}{r}.$

Hence, gain in potential energy from $r=R$ to $r=4R$ is $\Delta U = U_f - U_i = -\frac{GMm}{4R} - \left(-\frac{GMm}{R}\right).$

Simplify: $\Delta U = \frac{GMm}{R} - \frac{GMm}{4R} = \frac{3}{4}\frac{GMm}{R}.$

3. Use relation $GM = gR^2$

Since $g = \frac{GM}{R^2},$ we get $GM = gR^2.$

Therefore, $\Delta U = \frac{3}{4}\frac{gR^2 m}{R} = \frac{3}{4}mgR.$

4. Substitute values

$\Delta U = \frac{3}{4} \times 1 \times 10 \times 6.4 \times 10^6$ $\Delta U = \frac{3}{4} \times 64 \times 10^6$ $\Delta U = 48 \times 10^6\,\text{J}.$

5. Convert to MJ

Since $1\,\text{MJ} = 10^6\,\text{J}$, $\Delta U = 48\,\text{MJ}.$

6. Option check

• A: $48\,\text{MJ}$ ✅
• B: $24\,\text{MJ}$ ❌
• C: $36\,\text{MJ}$ ❌
• D: $12\,\text{MJ}$ ❌

Therefore, the correct option is A.