Question

A car of mass $50\text{kg}$ is travelling at a speed of $20\text{m/s}$ on a circular road of radius $30\text{m}$ having angle of banking equal to ${53}^{\circ }$. If the coefficient of static friction between the road and the tyres is $0.4$, then find the value of frictional force acting on the car. Take $g=10{\text{m/s}}^2$.

• A. $5\text{N}$
• B. $0\text{N}$
• C. $10\text{N}$
• D. $120\text{N}$

Answer 1

The correct option is B $0\text{N}$

Applying the condition of banking:-
$\tan \theta =\frac{v^2}{rg}$

Substituting the values as given in the question, we get:
$v=\sqrt{rg\tan \theta }=\sqrt{30\times 10\times \frac{4}{3}}\text{m/s}$
$\therefore v=20\text{m/s}$

Hence, only normal reaction will be sufficient enough to provide the centripetal force. Frictional force acting will be zero, because the car is already moving at the safe speed as per banking condition.