PhysicsThree rings, each of mass ‘M’ and radius ‘R’ are kept touching each other such that their centres form an equilateral triangle. The M.I. of the system about a median of the triangle is

Three rings, each of mass ‘M’ and radius ‘R’ are kept touching each other such that their centres form an equilateral triangle. The M.I. of the system about a median of the triangle is

  1. A

    3 MR2

  2. B

    3.5 MR2

  3. C

    2.5 MR2

  4. D

    2 MR2

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    Solution:

    Ring-1's moment of inertia with regard to the specified axis = m×r22_____(1)

    where r is the ring's radius and m is the ring's mass.

    By the parallel axis theorem, the moment of inertia of ring-2 with respect to the specified axis is = m×r22+m×r2=32m×r2______(2)

    similarly Ring-3's moment of inertia with respect to the specified axis, according to the parallel axis theorem

    =32m×r2_______(3)

    The system of combined rings' moment of inertia I is given by, I =32+32+12m×r2=72mr2

    Hence the correct answer 3.5MR2.

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