Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET202522 Apr 2025Morning ShiftPhysicsRotational MotionActual

A solid sphere and thin walled hollow sphere have same mass and same material. Which of them have greater moment of inertia about their diameter? [ I _ h = moment of inertia of hollow sphere about an axis coinciding with its diameter, I _ s = moment of inertia of solid sphere about an axis coinciding with its diameter]

Options

  1. AI _ s > I _ h
  2. BI _ h I _ s
  3. CI _ h > I _ s
  4. DI _ h = I _ s

Correct answer

C. I _ h > I _ s

Step-by-step solution

The moment of inertia depends on both the mass and its distribution relative to the rotation axis. For a solid sphere of mass M and radius R , the moment of inertia about a diameter is I_s = 2 5 MR^2 . For a thin-walled hollow sphere of equal mass and radius, the moment of inertia is I_h = 2 3 MR^2 . Since the mass in the hollow sphere is concentrated entirely at its outer surface, it is distributed farther from the axis of rotation. The coefficients confirm this relationship: 2 3 > 2 5 , so I_h > I_s . The hollow

Practice Rotational Motion on Quantrex Academy →

More from Rotational Motion

A bullet, fired into a door gets embedded exactly at it's centre, causing the door to rotate about it's vertical axis, practically without friction, with an angular velocity of 0.6 2026A singer, during his performance, stands on the edge of a circular turntable, and begins to walk along its edge with a speed of 1.5 ms⁻¹ relative to the ground. The turn table is m 2026A particle starts rotating from rest. The instantaneous angular displacement is = 3t^3 - t^2 , where is in radian and t in s; The angular velocity at t = 1 s is 2026Four masses each 2 kg are placed at the corners A, B, C, D of a mass less square frame. 40 kg mass is at the centre O of a square frame of side 0.2m. It is to be rotated about an a 2026The position of a particle of mass 1 kg at time t is given by r = t , i + j + 2t^2 , k , where t is in seconds and the coefficients have the proper units for r to be in metres. Wha 2026The angular momentum of a moving body remains constant, if 2026If the earth were to suddenly contract to half of its present radius, what would be the duration of the day? 2026The angular velocity of a body changes from 6 rad s ⁻¹ to 21 rad s ⁻¹ in a time of 1.5 s. If the moment of inertia of the body is 100 ~g ~m ^2 , then the rate of change of angular 2025 Full Rotational Motion list All MHT CET PYQs