Question

Given below are two statements: 
Statement (I): Planck's constant and angular momentum have the same dimensions. 
Statement (II): Linear momentum and moment of force have the same dimensions. 
In the light of the above statements, choose the correct answer from the options given below:

• A. Both Statement I and Statement II are false
• B. Statement I is true but Statement II is false
• C. Both Statement I and Statement II are true
• D. Statement I is false but Statement II is true

Answer 1

The Correct Option is B

Dimensions of Planck’s Constant (h):

Planck’s constant has dimensions of action (energy × time), which is equivalent to angular momentum:

\[ [h] = ML^2T^{-1} \]

Dimensions of Linear Momentum and Moment of Force:

Linear momentum has dimensions:

\[ [p] = MLT^{-1} \]

Moment of force (torque) has dimensions:

\[ [\tau] = ML^2T^{-2} \]

These are different, so Statement II is false.

Therefore, Statement I is true, and Statement II is false.