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JEE Main 202623 JanuaryMorning Shift
Exam
JEE Main
Year
2026
Date
23 January
Shift
Morning Shift
Subject
Physics
Chapter
Rotational Motion

JEE Main 2026 · 23 January · Morning Shift · Physics · Rotational Motion

Two small balls with masses m and 2 m are attached to both ends of...

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 :

Options

  1. A2L5md2\frac{2 L}{5 m d^{2}}
  2. B43Lmd2\frac{4}{3} \frac{L}{m d^{2}}
  3. C32Lmd2\frac{3}{2} \frac{L}{m d^{2}}
  4. D2Lmd2\frac{2 L}{m d^{2}}

Correct answer

C. 32Lmd2\frac{3}{2} \frac{L}{m d^{2}}

Step-by-step solution

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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