AIIMS 2019 Physics Collisions MCQ Question

In an inelastic collision, kinetic energy (K.E.) is not conserved, but momentum is. For the given bodies, the initial momentum is $p_i = (5 \times 10^3 \, \text{kg} \times 2 \, \text{m/s}) + (15 \times 10^3 \, \text{kg} \times 0) = 1 \times 10^4 \, \text{kg m/s}$. After the collision, the combined mass is $20 \times 10^3 \, \text{kg}$, and using momentum conservation, the final speed $v_f = \frac{p_i}{\text{total mass}} = \frac{1 \times 10^4}{20 \times 10^3} = 0.5 \, \text{m/s}$. The initial K.E. is $\frac{1}{2}(5 \times 10^3)(2^2) = 10 \, \text{kJ}$ and the final K.E. is $\frac{1}{2}(20 \times 10^3)(0.5^2) = 2.5 \, \text{kJ}$. Thus, the loss in K.E. is $ 10 , \text{kJ} - 2.5 , \text{kJ} =