Question

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

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

Answer 1

The correct option is B ${63.90}^{\circ }$

$r=20m$ , $v=20m/s$, $m=90kg$

let $R$ be the reaction force

using Force balance in Y and X direction

$F_y=0$

$Rcos\theta -mg=0$

$Rcos\theta =mg\dots \left(1\right)$

$F_x=m{a}_x$

$Rsin\theta =\frac{m{v}^2}{r}\dots \left(2\right)$

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

$tan\theta =\frac{v^2}{gr}$

$tan\theta =\frac{400}{9.8\times 20}$

$tan\theta =2.04$

$\theta =ta{n}^{-1}2.04$

$\theta ={63.90}^o$