MHTCET 22 Apr 2025 Shift 1 Paper

Concept:On curved roads, centripetal force changes the normal reaction acting on the vehicle.Explanation:Let $m$ be mass, $v$ be uniform speed, and $r$ be radius of curvature.On a horizontal road, normal reaction is:$$N = mg$$On a concave road, the normal reaction increases because it balances weight and provides the required centripetal force:$$N = \frac{mv^2}{r} + mg\cos\theta$$At the lowest point, $\cos\theta = 1$, so:$$N_{\max} = \frac{mv^2}{r} + mg$$Hence, $N > mg$ on a concave road.On a convex road, the normal reaction decreases because a part of the weight provides centripetal force:$$N = mg\cos\theta - \frac{mv^2}{r}$$At the top, $\cos\theta = 1$, so:$$N_{\max} = mg - \frac{mv^2}{r}$$Hence, $N < mg$ on a convex road.Comparing all three cases:$$mg + \frac{mv^2}{r} > mg > mg - \frac{mv^2}{r}$$Therefore, the normal reaction is maximum on the concave road.Answer:B. concave