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MHT CET202616 April 2026Evening ShiftPhysicsRotational MotionActual

Solid sphere is rotating about an axis as shown in figure. If the radius of the sphere is 5 cm, then radius of gyration about that axis will be x cm. The value of x is

Options

  1. A100
  2. B110
  3. C120
  4. D140

Correct answer

B. 110

Step-by-step solution

The moment of inertia of a solid sphere about an axis passing through its center of mass is given by I_ cm = 2 5 MR^2 . Using the parallel axis theorem, the moment of inertia about the given axis of rotation is: I = I_ cm + Md^2 where d is the distance from the axis of rotation to the center of mass of the sphere. Given R = 5 cm and d = 10 cm, we have: I = 2 5 M(5)^2 + M(10)^2 I = 10M + 100M = 110M The radius of gyration k is defined by I = Mk^2 . Mk^2 = 110M k^2 = 110 k = 110 cm Comparing this with x cm, we get x

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