Q. A car of mass $m$ moves on a banked road having radius $r$ and banking angle $\theta$. To avoid slipping from banked road, the maximum permissible speed of the car is $v_0$. The coefficient of friction $\mu$ between the wheels of the car and the banked road is
A) $\mu=\frac{v_0^2+rg\tan\theta}{rg+v_0^2\tan\theta}$
B) $\mu=\frac{v_0^2-rg\tan\theta}{rg-v_0^2\tan\theta}$
C) $\mu=\frac{v_0^2-rg\tan\theta}{rg+v_0^2\tan\theta}$
D) $\mu=\frac{v_0^2+rg\tan\theta}{rg-v_0^2\tan\theta}$
Explanation
[Solution by Dr. Abubacker] At maximum speed friction acts down the slope: $N\sin\theta+\mu N\cos\theta=\frac{mv_0^2}r$ and $N\cos\theta-\mu N\sin\theta=mg$. Dividing: $\frac{v_0^2}{rg}=\frac{\tan\theta+\mu}{1-\mu\tan\theta}$, so $\mu=\frac{v_0^2-rg\tan\theta}{rg+v_0^2\tan\theta}$. Answer (3).
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.