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Q)

A particle of mass m is travelling with a constant velocity $\overrightarrow {V} =V_0 \hat i$ along the line $y=b,z=0$. Let $dA$ be the area swept out by the position vector from the origin to the particle in time at end L be the magnitude of angular momentum of particle about orgin at any time t. Then 1) L= constant 2) $\large\frac{dA}{dt}=\frac{L}{m}$ 3) $\large\frac{dA}{dt}= \frac{2L}{m}$ 4) $\large\frac{dA}{dt}=\frac{L}{2m}$ Which of the following is correct?

a) 2,3 b) 1,2 c) 3,4 d) 1,4

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A)
As torque t= 0 dL/dt = 0

This implies L is a constant.  or 2m dA/dt = constant = L (because L = 2mxareal velocity)

Therefore dA/dt = L/2m

Hence option d is correct
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