Question

A circular racetrack of radius $300 \,m$ is banked at an angle of $15^°.$ The coefficient of friction between the wheels of a race car and the road is $0.2$. The optimum speed of the race car to avoid wear and tear on its tyres is
(Take$\, tan \,15^{\circ}=0.27, g=10\,m \,s^{-2}$)

• A. $10 \sqrt{3}\,m$ $s^{-1}$
• B. $9\sqrt{10}\,m$ $s^{-1}$
• C. $\sqrt{10}\,m$ $s^{-1}$
• D. $2 \sqrt{10} \,m$ $s^{-1}$

Answer 1

Answer: (B)

Here,$R=300 \,m$, $\theta=15^{\circ}$, $g=10\, m$ $s^{-2}$, $\mu=0.2$
The optimum speed of the car to avoid wear and tear is given by
$v=\sqrt{Rg \,tan\, \theta}$
$=\sqrt{300\times10\times tan\, 15^{\circ}}$
$=\sqrt{810}=9\sqrt{10}m$ $s^{-1}$