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

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

$I _{0}= I _{ com }+ MR ^{2}$
(Parallel Axis theorem)
$ I _{0}=\frac{2}{5} MR ^{2}+ MR ^{2}$
$ I _{0}=\frac{7}{5} MR ^{2}$
Hollow sphere

$I _{0}= I _{ com }+ MR ^{2}$
$=\frac{2}{3} MR ^{2}+ MR ^{2}=\frac{5}{3} MR ^{2}$

$I _{1}+ I _{2}+ I _{3}$ (Perpendicular axis theorem)
By symmetry MOI
About $1$" and $2$" Axis are same i.e.
$I_{1}=I_{2}$
$\therefore 2 I _{1}= I _{3}= MR ^{2}\left( I _{ com }= MR ^{2}\right)$
$I _{1}=\frac{ MR ^{2}}{2}$
Similarly in disc
$2 I_{1}=\frac{ MR ^{2}}{2}\left\{I_{c o m}=\frac{ MR ^{2}}{2}\right\}$
$I _{1}=\frac{ MR ^{2}}{4}$