Rotational Motion

JEE Main level, single correct, medium

193 of 280

Question 193 of 280

Two small balls with masses mm and 2 m are attached to both ends of a rigid rod of length dd and negligible mass. If angular momentum of this system is LL about an axis (AA) passing through its centre of mass and perpendicular to the rod then angular velocity of the system about AA is :

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Answer: (C) 32Lmd2\frac{3}{2} \frac{L}{m d^{2}}

CM from mass mm: xcm=2md3m=2d3x_{cm} = \frac{2md}{3m} = \frac{2d}{3}.
Distances: mm is 2d/32d/3 from CM, 2m2m is d/3d/3 from CM.
Icm=m(2d/3)2+2m(d/3)2=4md29+2md29=2md23I_{cm} = m(2d/3)^2 + 2m(d/3)^2 = \frac{4md^2}{9} + \frac{2md^2}{9} = \frac{2md^2}{3}.
L=Iω⇒ω=LI=3L2md2L = I\omega \Rightarrow \omega = \frac{L}{I} = \frac{3L}{2md^2}.

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