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.	\(\frac{1}{2}MR^2\)

Choose the correct answer from the options given below.

 

 

 

 

 

• A. A-II, B-I, 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

The Correct Option is A

To solve this problem, we need to match the items in List-I with their corresponding moments of inertia in List-II based on the given objects. The moment of inertia is a property that measures the resistance of a body to angular acceleration. Let's discuss each scenario:

1. Solid Sphere: For a solid sphere of radius \( R \) about any tangent, the formula for the moment of inertia is:
   • Moment of inertia, \( I = \frac{7}{5}MR^2 \)
   This matches option ii.
2. Hollow Sphere: For a hollow sphere of radius \( R \) about any tangent, the moment of inertia is:
   • Moment of inertia, \( I = \frac{5}{3}MR^2 \)
   This matches option i.
3. Circular Ring: The moment of inertia of a circular ring of radius \( R \) about its diameter is:
   • Moment of inertia, \( I = \frac{1}{2}MR^2 \)
   This matches option iv.
4. Circular Disc: The moment of inertia of a circular disc of radius \( R \) about any diameter is:
   • Moment of inertia, \( I = \frac{1}{4}MR^2 \)
   This matches option iii.

Based on the above analysis, the correct matching is:

• A. Solid Sphere: ii (\(\frac{7}{5}MR^2\))
• B. Hollow Sphere: i (\(\frac{5}{3}MR^2\))
• C. Circular Ring: iv (\(\frac{1}{2}MR^2\))
• D. Circular Disc: iii (\(\frac{1}{4}MR^2\))

Therefore, the correct option is: A-II, B-I, C-IV, D-III.