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MHT CET202520 Apr 2025Morning ShiftPhysicsRotational MotionActual

Two spheres each of mass M and radius R are connected with a massless rod of length 4 R . The moment of inertia of the system about an axis passing through the centre of one of the spheres and perpendicular to the rod will be

Options

  1. A21 5 MR ^2
  2. B84 5 MR ^2
  3. C42 5 MR ^2
  4. D5 21 MR ^2

Correct answer

B. 84 5 MR ^2

Step-by-step solution

Moment of inertia about an axis through the center of one sphere perpendicular to the rod The axis passes through the center of the first sphere, making its moment of inertia that of a solid sphere about its diameter: I₁ = 2 5 MR^2 . For the second sphere, apply the parallel axis theorem. The distance between centers is 4R , since the rod length of 4R is interpreted as center-to-center distance. The moment of inertia about the parallel axis is I₂ = 2 5 MR^2 + M(4R)^2 = 82 5 MR^2 . The total moment of inertia sums c

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