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 a circular disc of radius R about any diameter IV. $\frac{1}{2} {MR}^{2}$
Choose the correct answer from the options given below:

see full answer

Talk to JEE/NEET 2025 Toppers - Learn What Actually Works!

Real Strategies. Real People. Real Success Stories - Just 1 call away

An Intiative by Sri Chaitanya

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

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

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

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

answer is A.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

Solid sphere

$\begin{array}{l} I_{0} = I_{com} + {MR}^{2} \\ I_{0} = \frac{2}{5} {MR}^{2} + {MR}^{2} \\ I_{0} = \frac{7}{5} {MR}^{2} \end{array}$
Hollow sphere

$\begin{array}{l} I_{0} = I_{com} + {MR}^{2} \\ = \frac{2}{3} {MR}^{2} + {MR}^{2} = \frac{5}{3} {MR}^{2} \end{array}$

$I_{1} + I_{2} + I_{3}$ (Perpendicular axis theorem)
By symmetry

MOI about 1” and 2” Axis are same i.e.
$\begin{array}{l} I_{1} = I_{2} \\ ∴ 2 I_{1} = I_{3} = {MR}^{2} (I_{com} = {MR}^{2}) \\ I_{1} = \frac{{MR}^{2}}{2} \end{array}$
Similarly in disc
$\begin{array}{l} 2 I_{1} = \frac{{MR}^{2}}{2} \{I_{com} = \frac{{MR}^{2}}{2}\} \\ I_{1} = \frac{{MR}^{2}}{4} \end{array}$

Watch 3-min video & get full concept clarity

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Online Course for IIT JEE

Best Online Course for NEET

Best Online Course for CBSE

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Get Expert Academic Guidance – Connect with a Counselor Today!

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Online Course for IIT JEE

Best Online Course for NEET

Best Online Course for CBSE

	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 a circular disc of radius R about any diameter	IV.	$\frac{1}{2} {MR}^{2}$