Question bank/JEE Main/Physics

JEE MainPhysicsModerateRigid Body Dynamics

A uniform disc of mass m and radius R is resting on a smooth
horizontal surface and it is free to rotateabout its own axis which is
vertical. A small particle of mass m collides its periphery with a
velocity of Vin tangential direction. If the collision is perfectly in
elastic and the particle sticks to the periphery, theangular velocity of
the system just after the collision will be

Show answer and solution
Applying angular momentum conservation about the rotating axis
L_i = L_f
O + mv R= (mR22+mR2)ωf\left( \frac{mR^{2}}{2} + mR^{2} \right)\omega_{f}
ω=2V3R\omega = \frac{2V}{3R}

Source: Grass-G / P-07 Physics paper 17 October.docx

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