Question

Match List I with List II List I List II A. Spring constant I. (T-1) B. Angular speed II. (MT-2) C. Angular momentum III. (ML2) D. Moment of Inertia IV. (ML2T-1)

	List I		List II
A	Spring constant	I	(T-1)
B	Angular speed	II	(MT-2)
C	Angular momentum	III	(ML2)
D	Moment of Inertia	IV	(ML2T-1)

Choose the correct answer from the options given below:

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

Answer 1

The Correct Option is B

Solution:
Spring constant:
The spring constant \( K \) is given by: \[ [K] = \frac{[F]}{[x]} = \frac{MLT^{-2}}{L} = MT^{-2} \] Thus, spring constant has units of \( \boxed{MT^{-2}} \), which corresponds to List II.

Angular speed:
The angular speed \( \omega \) has dimensions: \[ [\omega] = \frac{[\theta]}{[t]} = \frac{1}{T} = T^{-1} \] Thus, angular speed has dimensions \( \boxed{T^{-1}} \), corresponding to List I.

Angular momentum:
Angular momentum \( L \) is given by: \[ [L] = [M][L][V] = ML^2T^{-1} \] Thus, Angular momentum has dimensions \( \boxed{ML^2T^{-1}} \), corresponding to List III.

Moment of inertia:
The moment of inertia \( I \) is: \[ [I] = [M][L]^2 = ML^2 \] Thus, moment of inertia has dimensions \( \boxed{ML^2} \), corresponding to List IV.

Thus, the correct match is \( A-II, B-I, C-III, D-IV \).