COMEDK 2025 Evening Solved Paper

Concept:The net force required to move the body up the incline must overcome the component of gravity along the plane, friction, and also provide the given acceleration.Explanation:Step 1: Identify forces acting along the incline.The weight component down the plane is $mg\sin\theta$.Here $m=10$ kg, $g=10$ m/s$^2$, $\theta=30^\circ$.So $mg\sin\theta = 10 \times 10 \times \sin30^\circ = 100 \times \frac12 = 50$ N.Step 2: Calculate the normal reaction $N$.$N = mg\cos\theta = 10 \times 10 \times \cos30^\circ = 100 \times \frac{\sqrt3}{2} = 50\sqrt3$ N.Step 3: Find the friction force $f$ opposing the upward motion.Friction $f = \mu N = \frac{\sqrt3}{6} \times 50\sqrt3 = \frac{50 \times 3}{6} = 25$ N.Step 4: Apply Newton’s second law along the incline. Let $P$ be the applied force up the plane.Net force = mass × acceleration: $P - (mg\sin\theta + f) = ma$.Thus $P = ma + mg\sin\theta + f$.Step 5: Substitute values.$ma = 10 \times 2 = 20$ N,$mg\sin\theta = 50$ N,$f = 25$ N.Therefore $P = 20 + 50 + 25 = 95$ N.Answer:95 N (Option D).