Question

A ball is rotating in circle of radius $r$ with constant speed $u\text{m/s}$ as shown in figure. When ball is at point $a$, find the magnitude of torque acting on ball about point $b$.

• A. $mu\text{N-m}$
• B. $m{u}^2\text{N-m}$
• C. $\frac{m}{u^2}\text{N-m}$
• D. $\frac{m}{u}\text{N-m}$

Answer 1

The correct option is B $m{u}^2\text{N-m}$


As speed of ball is constant therefore tengential acceleration$;a_t=0$.

We know,
Centripetal acceleration$;a_c=\frac{m{u}^2}{r}$.
and for uniform circular motion net force acting on ball will be directed toward centre
$\therefore F_{net}=m\frac{u^2}{r}$

$|\tau |$ due to $F_{net}$ about point $b=r_{\perp }.F_{net}=r.m\frac{u^2}{r}=m{u}^2\text{N-m}$