Systems of Particles and Rotational Motion
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Question : 10
Total: 33
(a) Find the moment of inertia of a sphere about a tangent to the sphere, given the moment of inertia of the sphere about any of its diameters to be
(b) Given the moment of inertia of a disc of mass M and radius R about any of its diameters to be
(b) Given the moment of inertia of a disc of mass M and radius R about any of its diameters to be
Solution:
(a) Moment of inertia of sphere about any diameter =
M R 2
Using parallel axes theorem,
Moment of inertia of sphere about a tangent to the sphere
=
M R 2 + M R 2 =
M R 2
(b) We are given, moment of inertia of the disc about any of its diameter=
M R 2
(i) Applying perpendicular axes theorem, moment of inertia of the disc about an axis passing through its centre and normal to the disc
= 2 ×
M R 2 =
M R 2
(ii) Applying parallel axes theorem, moment of inertia of the disc passing through a point on its edge and normal to the disc
=
M R 2 + M R 2 =
M R 2
Using parallel axes theorem,
Moment of inertia of sphere about a tangent to the sphere
(b) We are given, moment of inertia of the disc about any of its diameter
(i) Applying perpendicular axes theorem, moment of inertia of the disc about an axis passing through its centre and normal to the disc
(ii) Applying parallel axes theorem, moment of inertia of the disc passing through a point on its edge and normal to the disc
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