Question

A road is 5$m$ wide. Its radius of curvature is 50 m.The outer edge is above the inner edge of the road by a distance of $0.75m,$ if $g=10m/s^2$ then this road is most suited up to a velocity of :

• A. $\sqrt{300}m/s$
• B. $\sqrt{37.5}m/s$
• C. $\sqrt{75}m/s$
• D. $\sqrt{150}m/s$

Answer 1

The correct option is C $\sqrt{75}m/s$

$\begin{array}{c}\tan \theta =\frac{0.75}{5}\\ N\cos \theta =mg\\ N\sin \theta =\frac{m{v}^2}{R}\\ \Rightarrow V^2=Rg\tan \theta \\ V=\sqrt{\frac{50\times 10\times 0.75}{5}}\\ =\sqrt{75}m/s\\ Ans.\left(C\right)\end{array}$