Moment of inertia, radius of gyration, MI of simple objects
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See all →- A sphere of radius R is cut from a larger solid sphere of radius 2R as shown in the figure. The ratio of the moment of inertia of the smaller sphere to that of the rest part of the sphere about the Y-axis is : Answer: 3. 7/57 Key idea: moment of inertia of the remaining part = full sphere - removed sphere, using the parallel-axis theorem for the cu... 1
- The moment of inertia of a thin rod about an axis passing through its mid point and perpendicular to the rod is 2400 g cm^2. The length of the 400 g rod is nearly : Answer: 2. 8.5 cm Key idea: For a thin rod about its midpoint and perpendicular to its length, I=ML²/12 . L²=12I/M=12×2400/400=72 , so L=√(7... 1
- The ratio of radius of gyration of a solid sphere of mass M and radius R about its own axis to the radius of gyration of the thin hollow sphere of same mass and radius about its axis is : Answer: Dropped in the official answer key: full marks to every candidate Radius of gyration is k=√(I/M) . Solid sphere about its axis: I=2/... 1
- The ratio of the radius of gyration of a thin uniform disc about an axis passing through its centre and normal to its plane to the radius of gyration of the disc about its diameter is : Answer: 3. √(2) : 1 Radius of gyration is k=√(I/M) . For a disc, about the normal axis through the centre I=1/2MR² ; about a diameter I=1/4M... 1
- From a circular ring of mass 'M' and radius 'R' an arc corresponding to a 90° sector is removed. The moment of inertia of the remaining part of the ring about an axis passing through the centre of the ring and perpendicular to the plane of the ring i… Answer: 1. 3/4 Key idea: moment of inertia of a ring about its axis depends only on mass and radius, since every part is at distance R. Remo... 1
- Three objects, A : (a solid sphere), B : (a thin circular disk) and C : (a circular ring), each have the same mass M and radius R. They all spin with the same angular speed ω about their own symmetry axes. The amounts of work (W) required to bring th… Answer: 1. W_C>W_B>W_A Work needed to stop each body equals its rotational kinetic energy, W=1/2Iω² . Same M , R , ω , so W∝ I . Solid spher... 1