Question 206 of 210

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

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

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Answer: (A) $10.2$

At ${v}_{\max },f$ will be limiting in nature.
$∴$ Balancing force in vertical direction, $N\cos 30^{\circ}-mg-\mu N\cos 60^{\circ}=0$
$\Rightarrow N\left[\cos 30^{\circ}-\mu \cos 60^{\circ}\right]=mg$
$∴N=\dfrac{800\times 10}{(0.87-0.1)}\approx 10.2\times {10}^{3}kgm{s}^{-2}$
Hence, option $1.$