A particle is moving in a circular path of radius a, with a constant… | JEE Main 2014 (12 Apr, Shift 1)

Q75JEE Main 2014 · 12 APR · SHIFT 1Medium

Angular Momentum & its Conservation

A particle is moving in a circular path of radius a, with a constant velocity $v$ as shown in the figure. The center of circle is marked by 'C'. The angular momentum from the origin O can be written as:

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Answer: (a)

Angle at the centre is twice the angle at the circumference, so CP makes $2\theta$ with the x-axis.
$P=(a+a\cos2\theta,\ a\sin2\theta)$ ; tangential velocity $\vec v=v(-\sin2\theta,\ \cos2\theta)$ .
$L/m=xv_y-yv_x=va[(1+\cos2\theta)\cos2\theta+\sin^2 2\theta]$
$L/m=va(1+\cos2\theta)$ (options are written per unit mass).
So the answer is (a) $va(1+\cos2\theta)$ .

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