Question

78. A uniform disc of radius ‘a’ and mass 'm' is rotating freely with angular speed 'o' in a
horizontal plane, about a smooth fixed vertical axis through its centre. A particle of mass
'm' is then suddenly attached to the rim of the disc and rotates with it. The new angular
speed is:
3) w/ 15
4) w/3​

Answer 1

moment of inertia of disc about centre of mass, I = 1/2 ma²

where m is mass and a is radius of rim.

moment of inertia of system after attaching a particle of mass m on rim of the disc, I' = 1/2 ma² + ma² = 3ma²/2

there is no external torque acting on system of disc and particle.

so, initial angular momentum = final angular momentum

or, Iω = I'ω'

or, (1/2ma²)ω = (3/2ma²)ω'

or, ω' = ω/3

hence, new angular speed becomes ω/3.

Answer 2

Explanation:

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