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. $\frac{2}{5}M{R}^2$
ii. Uniform solid sphere of radius $R$	q. $\frac{2}{3}M{R}^2$
iii. Uniform rectangular lamina of length $l$ and breadth $b$	r. $M{R}^2$
iv. Thin uniform hollow sphere of radius $R$	s. $M\left(\frac{l^2+b^2}{12}\right)$

• A. $i-r,ii-q,iii-s,iv-p$
• B. $i-r,ii-p,iii-s,iv-q$
• C. $i-r,ii-p,iii-s,iv-p$
• D. $i-r,ii-q,iii-s,iv-q$

Answer 1

The correct option is B $i-r,ii-p,iii-s,iv-q$

$\left(i\right)$ $\text{MOI}$ of a thin uniform hollow cylinder passing through its centre and parallel to its length is given by
$I_{\text{com}}=M{R}^2$
$\left(ii\right)$ $\text{MOI}$ of a uniform solid sphere about an axis passing through its centre is given by
$I_{\text{com}}=\frac{2}{5}M{R}^2$
$\left(iii\right)$ $\text{MOI}$ of a uniform rectangular lamina of dimensions $(l\times b)$ about an axis which passes through its centre and perpendicular to its plane is
$I_{\text{com}}=\frac{M{l}^2}{12}+\frac{M{b}^2}{12}$
(where $l$ and $b$ are length and width of lamina)
$\left(iv\right)$ $\text{MOI}$ of a uniform hollow sphere about an axis, which passes through its centre is given by
$I_{\text{com}}=\frac{2}{3}M{R}^2$

Hence option $\left(b\right)$ gives the correct matching.