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Question: Average torque on a projectile of mass m, initial speed u and angle of projection q between initial ...

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

A

mu2sin⁡2θ2\frac{mu^{2}\sin 2\theta}{2}

B

mu2cosq

C

mu2 sinq

D

mu2cos⁡θ2\frac{mu^{2}\cos\theta}{2}

Answer

mu2sin⁡2θ2\frac{mu^{2}\sin 2\theta}{2}

Explanation

Solution

Li = 0, Lf = m × u sin q × R

\ DL = Lf

Now,

tav =ΔLΔt\frac{\Delta L}{\Delta t}=LfT\frac{L_{f}}{T}=musin⁡θR2usin⁡θg\frac{mu\sin\theta R}{\frac{2u\sin\theta}{g}}= mu2sin⁡2θ2\frac{mu^{2}\sin 2\theta}{2}