Question

A boy on a cycle pedals around a circle of 20 metres radius at a speed of 20 metres/sec. The combined mass of the boy and the cycle is $90kg$. The angle that the cycle makes with the vertical so that it may not fall is $(g = 9.8\mspace{6mu} m/\sec^{2})$

• A. $60.25^{o}$
• B. $63.90^{o}$
• C. $26.12^{o}$
• D. $30.00^{o}$

Answer 1

Answer: (B)

$63.90^{o}$

Answer 2

$r = 20m,$ $v = 20m/s,$ $m = 90kg,g = 9.8m/s^{2}$ (given)

$\theta = \tan^{- 1}\left( \frac{v^{2}}{rg} \right) = \tan^{- 1}\left( \frac{20 \times 20}{20 \times 10} \right) = \tan^{- 1}(2)$ $= 63.90{^\circ}$