Question

A cyclist leans with the horizontal at an angle of ${30}^o$, while negotiating round a circular road of radius $20\sqrt{3}$ meters. Speed of the cycle should be :

• A. $7\sqrt{3}m/s$
• B. $14m/s$
• C. $7\sqrt{6}m/s$
• D. $14\sqrt{3}m/s$

Answer 1

The correct option is D $14\sqrt{3}m/s$

Balancing the forces:

$N\sin 30°=mg⟶\left(1\right)$

and

$N\cos 30°=\frac{m{v}^2}{R}⟶\left(2\right)$

dividing $\left(2\right)$ by $\left(1\right)$

$\tan 30°=\frac{gR}{v^2}\Rightarrow v^2=\frac{gR}{\tan 30°}\Rightarrow v^2=10\times 20\sqrt{3}\times \sqrt{3}=200\times 3=600v=\sqrt{600}=24.5m/s=14\sqrt{3}m/s$