Rotation 2 Question 2

2. A thin smooth rod of length L and mass M is rotating freely with angular speed ω0 about an axis perpendicular to the rod and passing through its centre. Two beads of mass m and negligible size are at the centre of the rod initially. The beads are free to slide along the rod. The angular speed of the system, when the beads reach the opposite ends of the rod, will be

(2019 Main, 09 April II)

(a) Mω0M+3m

(b) Mω0M+m

(c) Mω0M+2m

(d) Mω0M+6m

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Answer:

Correct Answer: 2. (d)

Solution:

  1. As there is no external torque on system.

Angular momentum of system is conserved.

Iiωi=Ifωf

Initially,

Finally,

ML212ω0+0=ML212+2(m)L22ω

So, final angular speed of system is

ω=ML212ω0ML2+6mL212=Mω0M+6m



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