The normal reaction ' $\mathrm{N}$ ' for a vehicle of $800 \mathrm{~kg}$ mass, negotiating a turn on a $30^{\circ}$ banked road at maximum possible speed without skidding is__________ $\times 10^{3} \mathrm{~kg} \mathrm{~m} / \mathrm{s}^{2}$.
Correct Option: 1
At $\mathrm{v}_{\max }, \mathrm{f}$ will be limiting in nature.
$\therefore$ Balancing force in vertical direction,
$N \cos 30^{\circ}-\mathrm{mg}-\mu \mathrm{N} \cos 60^{\circ}=0$
$\Rightarrow \mathrm{N}\left[\cos 30^{\circ}-\mu \cos 60^{\circ}\right]=\mathrm{mg}$
$\therefore \mathrm{N}=\frac{800 \times 10}{(0.87-0.1)} \approx 10.2 \times 10^{3} \mathrm{~kg} \mathrm{~m} / \mathrm{s}^{2}$
Hence option $1 .$
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