Q125 / 160 · TS EAMCET 2024 (09 May Shift 1) · Physics

A car is moving on circular track banked at an angle of $45^{\circ}$. If the maximum permissible speed of the car to avoid slipping is twice the optimum speed of the car to avoid the wear and tear of the tyres, then the coefficient of static friction between the wheels of the car and the road is

  • A
    0.3
  • B
    0.5
  • C
    0.4
  • Correct answer
    D
    0.6

Solution

Maximum speed $V_{\max }=\sqrt{\frac{r g(\mu+\tan \theta)}{1-\mu \tan \theta}}$ and optimum speed $V_{\mathrm{o}}=\sqrt{\mathrm{rg} \tan \theta}$ Given $\theta=45^{\circ}$ and $V_{\max }=2 V_0$ $\sqrt{\frac{\operatorname{rg}(\mu+\tan \theta)}{1-\mu \tan \theta}}=2 \sqrt{\operatorname{rg} \tan \theta}$ Squaring both sides $\frac{(\mu+\tan \theta)}{(1-\mu \tan \theta)}=4 \tan \theta$ $\begin{aligned} & \Rightarrow \frac{\mu+\tan 45^{\circ}}{1-\mu \tan 45^{\circ}}=4 \tan 45^{\circ} \Rightarrow \frac{\mu+1}{1-\mu}=4 \\ & \Rightarrow \mu+1=4-4 \mu \Rightarrow 5 \mu=3 \therefore \mu=\frac{3}{5}=0.6 \end{aligned}$

Hence, the correct answer is option: 'D'.

Relevant Questions