Question

A cycle is going on an overbridge of radius $R$. The driver maintains a constant speed. As the cycle is ascending on the overbridge, the normal force on it:

• A. increases
• B. decreases
• C. remains the same
• D. fluctuates

Answer 1

The correct option is A increases


As we know that, normal force will pass through the centre of the bridge., and net force towards the centre of overbridge is

$F_{centre}=mg\cos \theta -N\left(\text{From FBD}\right)$

And here, $F_{centre}$ is the responsible for the circular motion. So

$mg\cos \theta -N=\frac{m{v}^2}{R}$

$\Rightarrow N=mg\cos \theta -\frac{m{v}^2}{R}$

Since, $m,R,g$ and speed $v$ are constant.

$\therefore N$ increases with $\cos \theta$

When ascending, $\theta$ will decrease, so $\cos \theta$ will increase means normal force increases.

Why this question ? Tip: In this question, we can observe how normal force changes in vertical circular motion.