Question

The vertical section of a road over a canal bridge in the direction of its length is in the form of circle of radius $8.9m$. Then the greatest speed at which the car can cross this bridge without losing contact with the road at its highest point, the centre of gravity of the car being at a height $h=1.1m$ from the ground (Take $g=10m/se{c}^2$)

• A. $5m/sec$
• B. $10m/sec$
• C. $15m/sec$
• D. $20m/sec$

Answer 1

Answer: (B)

$10m/sec$

Given : Radius of the circular arc $r=8.9$ m $g=10m/s^2$

Heigh of centre of gravity of car above the road $h=1.1$ m

Centre of gravity of the car is revolving in a circular motion.

$\therefore$ Distance of centre of gravity of car and the centre of circle $l=r+h=8.9+1.1=10$ m

Using $\frac{m{v}^2}{l}=mg-N$

For maximum speed of car $\left(v_{max}\right)$, $⟹N=0$

$\therefore$ $\frac{m{v}_{max}^2}{l}=mg$

OR $\frac{m{v}_{max}^2}{10}=m\times 10$ $⟹v_{max}=10$ $m/s$