Q126 / 160 · AP EAMCET 2022 (06 Jul Shift 1) · Physics

The coefficient of static friction between the road and tyres of a car is 0.4 . The maximum permissible speed of the car is $10 \mathrm{~ms}^{-1}$ on curved unbanked road. Then the maximum radius of curvature of the road is (acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ )

  • A
    $10 \sqrt{5} \mathrm{~m}$
  • Correct answer
    B
    $25 \mathrm{~m}$
  • C
    $20 \sqrt{2} \mathrm{~m}$
  • D
    $30 \mathrm{~m}$

Solution

The necessary centripetal force is provided by friction force $\begin{aligned} & \text { So, } \frac{\mathrm{mV}^2}{\mathrm{r}}=\mu \mathrm{mg} \\ & \Rightarrow \mathrm{V}=\sqrt{\mu \mathrm{rg}} \\ & \Rightarrow 10=\sqrt{0.4 \times \mathrm{r} \times 10} \\ & \Rightarrow 100=4 \mathrm{r} \\ & \Rightarrow \mathrm{r}=25 \mathrm{~m}\end{aligned}$

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

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