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Question

Column I of the following table gives a list of bodies and column II gives their moments of inertia about the axis of symmetry passing through their centre of mass. Assume mass of each of the bodies is M. Then identify the correct matching.

Column-I Column-II
i. Thin uniform hollow cylinder of radius R p. 25MR2
ii. Uniform solid sphere of radius R q. 23MR2
iii. Uniform rectangular lamina of length l and breadth b r. MR2
iv. Thin uniform hollow sphere of radius R s. M(l2+b212)

A
ir,iiq,iiis,ivp
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B
ir,iip,iiis,ivq
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C
ir,iip,iiis,ivp
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D
ir,iiq,iiis,ivq
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Solution

The correct option is B ir,iip,iiis,ivq
(i) MOI of a thin uniform hollow cylinder passing through its centre and parallel to its length is given by
Icom=MR2
(ii) MOI of a uniform solid sphere about an axis passing through its centre is given by
Icom=25MR2
(iii) MOI of a uniform rectangular lamina of dimensions (l×b) about an axis which passes through its centre and perpendicular to its plane is
Icom=Ml212+Mb212
(where l and b are length and width of lamina)
(iv) MOI of a uniform hollow sphere about an axis, which passes through its centre is given by
Icom=23MR2

Hence option (b) gives the correct matching.

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