Q. A circular road of radius $1000\ m$ has banking angle $45{^\circ}.$ The maximum safe speed of a car having mass $2000\ kg$ will be, if the coefficient of friction between tyre and road is 0.5
A) $172\ m/s$
B) $124\ m/s$
C) $99\ m/s$
D) $86\ m/s$
Explanation
(a) The maximum velocity for a banked road with friction,
$v^{2} = gr\left( \begin{array}{r}
\frac{\mu + \tan\theta}{1 - \mu\tan\theta} \\
\
\end{array} \right)$
$\Rightarrow v^{2} = 9.8 \times 1000 \times \left( \begin{array}{r}
\frac{0.5 + 1}{1 - 0.5 \times 1} \\
\
\end{array} \right) \Rightarrow v = 172m/s$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.