Question

Match List-I with List-II

List I		List II
A	Moment of inertia of solid sphere of radius R about any tangent	I	$\frac{5}{3}M{R}^2$
B	Moment of inertia of hollow sphere of radius (R) about any tangent	II	$\frac{7}{5}M{R}^2$
C	Moment of inertia of circular ring of radius (R) about its diameter.	III	$\frac{1}{4}M{R}^2$
D	Moment of inertia of circular disc of radius (R) about any diameter.	IV	$\frac{1}{2}M{R}^2$

Question: Choose the correct answer from the options given below

• A. A-II, B-II, C-IV, D-III
• B. A-I, B-II, C-IV, D-III
• C. A-II, B-I, C-III, D-IV
• D. A-I, B-II, C-III, D-IV

Answer 1

Answer: (A)

Solid sphere

$I_0=I_{com}+M{R}^2$
(Parallel Axis theorem)
$I_0=\frac{2}{5}M{R}^2+M{R}^2$
$I_0=\frac{7}{5}M{R}^2$
Hollow sphere

$I_0=I_{com}+M{R}^2$
$=\frac{2}{3}M{R}^2+M{R}^2=\frac{5}{3}M{R}^2$

$I_1+I_2+I_3$ (Perpendicular axis theorem)
By symmetry MOI
About $1$" and $2$" Axis are same i.e.
$I_1=I_2$
$\therefore 2I_1=I_3=M{R}^2\left(I_{com}=M{R}^2\right)$
$I_1=\frac{M{R}^2}{2}$
Similarly in disc
$2I_1=\frac{M{R}^2}{2}\left\{I_{com}=\frac{M{R}^2}{2}\right\}$
$I_1=\frac{M{R}^2}{4}$