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Question: A smooth uniform rod of length L and mass M has two identical beads of negligible size, each of mass...

A smooth uniform rod of length L and mass M has two identical beads of negligible size, each of mass m, which can slide freely along the rod. Initially, the two beads are at the centre of the rod and the system is rotating with angular velocity w0 about an axis perpendicular to rod and passing through the mid-point of rod. There are no external forces. When the beads reach the ends of the rod the angular velocity of the system is –

A

MM+3m\frac{M}{M + 3m}w0

B

MM+6m\frac{M}{M + 6m}w0

C

M+6mM\frac{M + 6m}{M}w0

D

w0

Answer

MM+6m\frac{M}{M + 6m}w0

Explanation

Solution

I1w1 = I2w2

ML212\frac{ML^{2}}{12}w0 = [ML212+m(L2)2+m(L2)2]ω′\left\lbrack \frac{ML^{2}}{12} + m\left( \frac{L}{2} \right)^{2} + m\left( \frac{L}{2} \right)^{2} \right\rbrack\omega'Ž w' = MM+6mω0\frac{M}{M + 6m}\omega_{0}