A road is banked at an angle of $30^o$ to the horizontal for negotiating a curve of radius $10\sqrt 3 m$. At what velocity will a car experience no friction while negotiating the curve? ............... $km/hr$
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$\tan \theta=\frac{v^{2}}{r g}$
$\Rightarrow \tan 30^{\circ}=\frac{v^{2}}{(10 \sqrt{3})(10)}$
$\Rightarrow v^{2}=100 \mathrm{ms}^{-1} \Rightarrow v=10 \mathrm{ms}^{-1}$
$\Rightarrow v=10 \times \frac{18}{5} k m h r^{-1}=36 k m h r^{-1}$
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