Q101 / 150 · MHT CET 2025 (22 Apr Shift 1) · Physics

A vehicle is moving with uniform speed along 3 different shaped roads as horizontal, concave and convex. The surface of road on which, the normal reaction on vehicle is maximum is

  • A
    convex
  • Correct answer
    B
    concave
  • C
    horizontal
  • D
    same on all the 3 surface

Solution

The normal reaction on the vehicle is determined by analyzing the forces when moving at uniform speed v on different surfaces.

On a horizontal road, the gravitational force mg is balanced by the normal reaction NH, giving NH = mg.

At the lowest point on a concave road, the centripetal force mv2/r is provided by the normal reaction exceeding gravity: NC − mg = mv2/r, leading to NC = mg + mv2/r.

At the highest point on a convex road, gravity exceeds the normal reaction to provide the centripetal force: mg − NX = mv2/r, so NX = mg − mv2/r.

Comparing the expressions shows NC > NH > NX, indicating the maximum normal reaction occurs on the concave road.

The answer is $\boxed{B}$.

Hence, the correct answer is option: 'B'.

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