Question

Match List-I with List-II 

List-I	Body / Axis	List-II	Moment of Inertia
A	M.I. of solid cone about its vertical axis	IV	\(\dfrac{3}{10}MR^2\)
B	M.I. of solid cylinder about its own axis	III	\(\dfrac{1}{2}MR^2\)
C	M.I. of circular lamina about a diameter	II	\(\dfrac{1}{4}MR^2\)
D	M.I. of annular ring about a diameter	I	\(\dfrac{1}{4}M(R^2+r^2)\)

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

Hint:

For moment of inertia, always identify both the body and the axis of rotation carefully.

Answer 1

The Correct Option is B

Concept:
Moment of inertia depends on mass distribution about the axis of rotation.

Step 1: Solid cone about vertical axis.
Moment of inertia of a solid cone about its vertical axis is: \[ I=\frac{3}{10}MR^2 \] So, \[ A\rightarrow IV \]

Step 2: Solid cylinder about own axis.
Moment of inertia of a solid cylinder about its own axis is: \[ I=\frac{1}{2}MR^2 \] So, \[ B\rightarrow III \]

Step 3: Circular lamina about diameter.
Moment of inertia of circular lamina about a diameter is: \[ I=\frac{1}{4}MR^2 \] So, \[ C\rightarrow II \]

Step 4: Annular ring about diameter.
Moment of inertia of annular ring about a diameter is: \[ I=\frac{1}{4}M(R^2+r^2) \] So, \[ D\rightarrow I \] Therefore: \[ A-IV,\ B-III,\ C-II,\ D-I \] \[ \therefore \text{Correct Answer is (B)} \]