# A massless rod S having length 2l has point masses attached to its two each as shown in Fig. The rod is rotating about an axis passing through its

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A massless rod S having length 2l has point masses attached to its two each as shown in Fig. The rod is rotating about an axis passing through its centre and making angle alpha with the axis. The magnitude of rate of change of momentum of rod i.e. |(dL)/(dt)| equals

A. 2 ml^(3) omega^(2) sin alpha. Cos alpha
B. ml^(2)omega^(2) sin 2 alpha
C. ml^(2) sin 2 alpha
D. m^(1//2)l^(1//2) omega sin alpha. cos alpha

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Correct Answer - B
Refer to Fig.

The radius r of the circle traced by the masses is r = l sin alpha
Angular momentum overset rarr(L) = overset rarr(r ) xx m overset rarr(v)
|overset rarr(L)| = r xx m omega r = m omega r^(2)
= momega (l sin alpha)^(2) = m omegal^(2) sin^(2)alpha
(dL)/(dt) = m omegal^(2) sin alpha cos alpha(d alpha)/(dt)
= m omegal^(2) (sin 2 alpha) omega = m omega^(2)l^(2) sin 2 alpha