Question

A motorcycle is going on an over-bridge of radius R at a constant speed. As the motorcycle is ascending on the over-bridge, the normal force on it.

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

Answer 1

The correct option is A increases

Lets take 3 points on the ascending side of the circular bridge

The motorcycle is going with constant velocity.

So it will have a centripetal acceleration of $\frac{v^2}{R}$ always

$\Rightarrow$ At A: mg cos ${\theta }_2-N_A$ = $\frac{m{v}^2}{R}$

$N_A=mgcos{\theta }_2-\frac{m{v}^2}{R}$ ......... (i)

Similarly

$N_B=mgcos{\theta }_1-\frac{m{v}^2}{R}$ ......... (ii)

$N_C=mg-\frac{m{v}^2}{R}$ ( at topmost point ) ....... (iii)

${\theta }_2>{\theta }_1$

So cos ${\theta }_2<cos{\theta }_1$

now comparing all 3 equations we get

$N_C>N_B>N_A$

So as the motorcycle is going up, the normal on it by bridge is increasing.