Q.

A rod of mass ‘M’ and length 6R is pivoted at its centre (point P) to rotate in vertical plane as shown. Two discs of same radius ‘R’ are joined at the ends  O1 and  O2 of the rod. Mass of the discs A and B are ‘M’ and ‘2M’ respectively. Initial angular velocities of discs are shown in figure. The system is released from rest from horizontal position. The angular velocity of the rod when it is vertical is gλR . Find the value of  λ.

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answer is 5.

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Detailed Solution

Since, all forces acting on discs are passing through their centers, angular speeds of discs will not change.From conservation of energychange in potential energy = Rotational kinetic energy of the rod ⇒∆PE= Itotal ω22      Where Itotal = total moment of inertia of the system⇒(2Mg3R)−(Mg3R)=12M(6R)212+M(3R)2+2M{3R}2ω2⇒3MgR=1230MR2ω2=15MR2ω2⇒3MgR=15MR2ω2⇒ω=g5R
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