Question

Average torque on a projectile of mass $m$, initial speed $u$ and angle of projection $\theta$ between initial and final positions $P$ and $Q$ about the point of projection is

• A. $\frac{m{u}^{2}sin2\theta }{2}$
• B. $m{u}^{2}cos\theta$
• C. $m{u}^{2}sin\theta$
• D. $\frac{m{u}^{2}cos\theta }{2}$

Answer 1

The correct option is A $\frac{m{u}^{2}sin2\theta }{2}$

Torque at a general point $=$ Horizontal distance covered $\times$ m g (as we only take r perpendicular to g)
$\therefore \tau =mg\times ucos\theta t$ ......(1)
$t=\frac{usin\theta }{g}$
Substituting t in (1), we get $\tau =\frac{m{u}^2\sin 2\theta }{2}$