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

For solid sphere ![JEE Main 2022 Physics, Rotational Motion — solution figure 1](https://prepforbharat.s3.ap-south-1.amazonaws.com/exam/615f0e999476412f48314daf/Physics/images/Rotational_Motion/648b5a6e417cc3fb48d67cd6/solution_1__q_648b5a6e417cc3fb48d67cd6__cdn-question-pool.getmarks.app__9b482886-249b-42d9-ae6e-2018a8de370c-image__c50a7d6501_final_ppt_sync.png) ${I}_{0}={I}_{\mathrm{com}}+M{R}^{2}$ (Using parallel axis theorem) ${I}_{0}=\frac{2}{5}M{R}^{2}+M{R}^{2}$ ${I}_{0}=\frac{7}{5}M{R}^{2}$$\Rightarrow A\rightarrow II$ For hollow sphere ![JEE Main 2022 Physics, Rotational Motion — solution figure 2](https://prepforbharat.s3.ap-south-1.amazonaws.com/exam/615f0e999476412f48314daf/Physics/images/Rotational_Motion/648b5a6e417cc3fb48d67cd6/solution_1__q_648b5a6e417cc3fb48d67cd6__cdn-question-pool.getmarks.app__9b482886-249b-42d9-ae6e-2018a8de370c-image__c50a7d6501_final_ppt_sync.png) $I={I}_{\mathrm{com}}+M{R}^{2}\Rightarrow I=\frac{5}{3}M{R}^{2}\Rightarrow B\rightarrow I$ For Circular ring ![JEE Main 2022 Physics, Rotational Motion — solution figure 3](https://prepforbharat.s3.ap-south-1.amazonaws.com/exam/615f0e999476412f48314daf/Physics/images/Rotational_Motion/648b5a6e417cc3fb48d67cd6/solution_2__q_648b5a6e417cc3fb48d67cd6__cdn-question-pool.getmarks.app__5efac0a7-111e-4477-bce2-9be673721334-image__bb00a880f2_final_ppt_sync.png) ${I}_{1}+{I}_{2}={I}_{3}$ ( Using perpendicular axis theorem) By symmetry MOI About $1$ and $2$ Axis are same i.e. ${I}_{1}={I}_{2}$ $\therefore 2{I}_{1}={I}_{3}=M{R}^{2}(\because {I}_{com}=M{R}^{2})$ ${I}_{1}=\frac{M{R}^{2}}{2}\Rightarrow C\rightarrow IV$ Similarly in disc $2{I}_{1}=\frac{M{R}^{2}}{2}{\because {I}_{\mathrm{com}}=\frac{M{R}^{2}}{2}}$ ${I}_{1}=\frac{M{R}^{2}}{4}\Rightarrow D\rightarrow III$

Match List-I with List-II List-I List-II… - JEE Main 2022 Physics PYQ

JEE Main 2022 — Physics Mechanics

2022mcqmedium

Match List-I with List-II

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

Official previous-year question

Held on 28 Jun 2022 · Verified 6 Jul 2026.

Options

A
$A-\mathrm{II},B-I,C-\mathrm{IV},D-\mathrm{III}$
B
$A-I,B-\mathrm{II},C-\mathrm{IV},D-\mathrm{III}$
C
$A-\mathrm{II},B-I,C-\mathrm{III},D-\mathrm{IV}$
D
$A-I,B-\mathrm{II},C-\mathrm{III},D-\mathrm{IV}$

Did you get this right?

Solution

For solid sphere

JEE Main 2022 Physics, Rotational Motion — solution figure 1

${I}_{0}={I}_{\mathrm{com}}+M{R}^{2}$ (Using parallel axis theorem)

${I}_{0}=\frac{2}{5}M{R}^{2}+M{R}^{2}$

${I}_{0}=\frac{7}{5}M{R}^{2}$ $\Rightarrow A\rightarrow II$

For hollow sphere

JEE Main 2022 Physics, Rotational Motion — solution figure 2

$I={I}_{\mathrm{com}}+M{R}^{2}\Rightarrow I=\frac{5}{3}M{R}^{2}\Rightarrow B\rightarrow I$

For Circular ring

JEE Main 2022 Physics, Rotational Motion — solution figure 3

${I}_{1}+{I}_{2}={I}_{3}$ ( Using perpendicular axis theorem)

By symmetry MOI

About $1$ and $2$ Axis are same i.e.

${I}_{1}={I}_{2}$

$\therefore 2{I}_{1}={I}_{3}=M{R}^{2}(\because {I}_{com}=M{R}^{2})$

${I}_{1}=\frac{M{R}^{2}}{2}\Rightarrow C\rightarrow IV$

Similarly in disc

$2{I}_{1}=\frac{M{R}^{2}}{2}{\because {I}_{\mathrm{com}}=\frac{M{R}^{2}}{2}}$

${I}_{1}=\frac{M{R}^{2}}{4}\Rightarrow D\rightarrow III$

Your note

JEE Main Mechanics in other years

Mechanics 2026 Mechanics 2025 Mechanics 2024 Mechanics 2023 Mechanics 2021 Mechanics 2020 Mechanics 2019 Mechanics 2018 Mechanics 2017 Mechanics 2016 Mechanics 2015 Mechanics 2014

More JEE Main Mechanics questions

A small bob $A$ of mass $m$ is attached to a massless rigid rod of length 1 m pivoted at point $P$ and kept at an angle of $60^{\circ}$ with vertical as shown in figure. At distance of 1 m below point $P$, an identical bob $B$ is kept at rest on a smooth horizontal surface that extends to a circular track of radius $R$ as shown in figure. If bob $B$ just manages to complete the circular path of radius $R$ upto a point $Q$ after being hit elastically by $\operatorname{bob} A$, then radius $R$ is $\_\_\_\_$ m. ![JEE Main 2026 Physics, Work Power Energy — question figure](https://prepforbharat.s3.ap-south-1.amazonaws.com/exam/615f0e999476412f48314daf/Physics/images/Work_Power_Energy/6983c1948bfdbb243563967c/question_1__q_6983c1948bfdbb243563967c__cdn-question-pool.getmarks.app__23S1_q_33_1__f4c94b6bfa_final_ppt_sync.png)

2026hard

In a screw gauge the zero of main scale reference line coincides with the fifth division of the circular scale when two studs are in contact. There are $100$ divisions in circular scale and pitch of screw gauge is $0.1$ mm. When diameter of a sphere is measured, the reading of main scale is $5$ mm and $50^{\text{th}}$ division of circular scale coincides with the reference line of main scale. The diameter of sphere is _______ mm.

2026medium

Two masses $m$ and 2 m are connected by a light string going over a pulley (disc) of mass 30 m with radius $r=0.1 \mathrm{~m}$. The pulley is mounted in a vertical plane and it is free to rotate about its axis. The 2 m mass is released from rest and its speed when it has descended through a height of 3.6 m is $\_\_\_\_$ $\mathrm{m} / \mathrm{s}$. (Assume string does not slip and $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}$)

2026medium

Water flows through a horizontal tube as shown in the figure. The difference in height between the water columns in vertical tubes is 5 cm and the area of cross-sections at $A$ and $B$ are $6 \mathrm{~cm}^{2}$ and $3 \mathrm{~cm}^{2}$ respectively. The rate of flow will be $\_\_\_\_$ $\mathrm{cm}^{3} / \mathrm{s}$. (take $g=10 \mathrm{~m} / \mathrm{s}^{2}$) ![JEE Main 2026 Physics, Mechanical Properties of Fluids — question figure](https://prepforbharat.s3.ap-south-1.amazonaws.com/exam/615f0e999476412f48314daf/Physics/images/Mechanical_Properties_of_Fluids/6983c1798bfdbb243563954b/question_1__q_6983c1798bfdbb243563954b__cdn-question-pool.getmarks.app__21S1_q_26_1__d7484b314f_final_ppt_sync.png)

2026medium

Two circular discs of radius each 10 cm are joined at their centres by a rod of length 30 cm and mass 600 gm as shown in figure. If the mass of each disc is 600 gm and applied torque between two discs is $43 \times 10^{5}$ dyne. cm, the angular acceleration of the discs about the given axis $A B$ is $\_\_\_\_$ $\mathrm{rad} / \mathrm{s}^{2}$. ![JEE Main 2026 Physics, Rotational Motion — question figure](https://prepforbharat.s3.ap-south-1.amazonaws.com/exam/615f0e999476412f48314daf/Physics/images/Rotational_Motion/6983c1ab8bfdbb24356397a7/question_1__q_6983c1ab8bfdbb24356397a7__cdn-question-pool.getmarks.app__28S1_q_32_1_v2__3064f7e74b_final_ppt_sync.png)

2026medium

View all Mechanics questions

Keep practicing Mechanics

Work through every JEE Main Mechanics PYQ, year by year.

Browse all Physics topics

Options

Did you get this right?

Solution

Your note

JEE Main Mechanics in other years

More JEE Main Mechanics questions

Other Physics topics for JEE Main

Electromagnetism

Modern Physics

Optics

Thermodynamics

Waves & Oscillations

Keep practicing Mechanics