A motor vehicle of mass $1000 \mathrm{~kg}$ is moving on a circular road having banking angle $30^{\circ}$…

A motor vehicle of mass $1000 \mathrm{~kg}$ is moving on a circular road having banking angle $30^{\circ}$ and coefficient of friction 0.2 . Then the normal reaction force on the motor vehicle is about (Acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ )
  1. $6750 \mathrm{~N}$
  2. $9060 \mathrm{~N}$
  3. $1070 \mathrm{~N}$
  4. $13055 \mathrm{~N}$

Solution

Mass of motor vehicle, $\mathrm{m}=1000 \mathrm{~kg}$ Banking angle, $\theta=30^{\circ}$ Coefficient of friction, $\mu=0.2$
$\begin{aligned} & N \cos \theta=m g+f \sin \theta \\ & \text { Here } f=\mu N \\ & N \cos \theta=m g+\mu N \sin \theta \\ & \frac{N \sqrt{3}}{2}=1000 \times 10+0.2 N \times \frac{1}{2} \\ & N\left[\frac{\sqrt{3}}{2}-\frac{1}{10}\right]=10000\end{aligned}$ Normal reaction force, $\mathrm{N}=13055 \mathrm{~N}$

Asked in: AP EAMCET 2023 (17 May Shift 2)

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