First slide

Torque

Question

Average torque on a projectile of mass m (initial speed u and angle of projection $θ$ ) between initial and final positions P and Q as shown in figure, about the point of projection is:

Moderate

A

$\frac{{mu}^{2} \sin 2 θ}{2}$
B

$\frac{{mu}^{2} cosθ}{2}$
C

${mu}^{2} \sin θ$
D

${mu}^{2} \cos θ$

Solution

$\vec{τ_{av}} . ∆ t = ∆ L - - - - - - (i)$
Here $∆ t = time of flight = \frac{2 u \sin θ}{g}$
Change in angular momentum about point of projection (initially it is zero)
$| \vec{∆ L} | = | {\vec{L}}_{f} - \vec{L_{i}} | = (mu \sin θ) Range$
= $\frac{(mu \sin θ) (u^{2} \sin 2 θ)}{g} = \frac{{mu}^{3} \sin θ \sin 2 θ}{g}$
Now $| {\vec{τ}}_{av} | = | \frac{\vec{∆ L}}{∆ t} | = \frac{{mu}^{3} \sin θ \sin 2 θ}{g} \times \frac{g}{2 u \sin θ}$
= $\frac{{mu}^{2} \sin 2 θ}{2}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App