Question

The normal reaction $\text{N}$ for a vehicle of $800\text{kg}$ mass, negotiating a turn on a ${30}^{\circ }$ banked road at maximum possible speed without skidding is _____ $\times {10}^3{\text{kg-m/s}}^2$.

Take $\cos {30}^{\circ }=0.87$ and $\mu =0.2$

• A. $10.2$
• B. $7.2$
• C. $12.4$
• D. $6.96$

Answer 1

The correct option is A $10.2$


At maximum possible speed, friction will be limiting in nature.

$\therefore$ Balancing the forces in vertical direction,

$N\cos {30}^{\circ }-mg-\mu N\cos {60}^{\circ }=0$

$\Rightarrow N(\cos {30}^{\circ }-\mu \cos {60}^{\circ })=mg$

$\Rightarrow N=\frac{mg}{\cos {30}^{\circ }-\mu \cos {60}^{\circ }}$

$\Rightarrow N=\frac{800\times 9.8}{(0.87-0.2\times 0.5)}\approx 10.2\times {10}^3{\text{kg-m/s}}^2$

Hence, option $\left(A\right)$ is the correct answer.