COMEDK 2025 Morning Solved Paper

Concept:The net work done equals the sum of work done by gravity and work done by the spring force.Explanation:Step 1: Determine total vertical displacement.The ball falls $2\ \text{m}$ before hitting the spring, then compresses it by $0.5\ \text{m}$.Total height drop: $2.0\ \text{m} + 0.5\ \text{m} = 2.5\ \text{m}$.Step 2: Compute work done by gravity.Gravity acts downward, in the direction of motion.$W_g = m g \Delta h = (0.5\ \text{kg})(10\ \text{m/s}^2)(2.5\ \text{m}) = 12.5\ \text{J}$.Step 3: Compute work done by the spring.The spring force opposes the compression, so work is negative.$W_s = -\frac{1}{2} k x^2 = -\frac{1}{2} (24\ \text{N/m})(0.5\ \text{m})^2 = -3.0\ \text{J}$.Step 4: Add the works to find net work.$W_{\text{net}} = W_g + W_s = 12.5\ \text{J} - 3.0\ \text{J} = 9.5\ \text{J}$.Answer:Option D ($9.5\ \text{J}$).