Question

Dimensional formula of Planck’s constant is similar to

• A. Angular momentum
• B. Linear momentum
• C. Force
• D. Velocity

Hint:

Remember, Planck’s constant has the same dimensions as angular momentum, which involves the product of position and momentum, both of which have dimensions of mass, length, and time.

Answer 1

The Correct Option is A

Planck's constant \( h \) has dimensions of action, which is the product of energy and time. The dimensional formula of Planck's constant is: \[ [h] = \text{M L}^2 \text{T}^{-1} \] Now, let’s examine the dimensional formulas of the options: - Angular momentum has the dimensional formula of: \[ [L] = \text{M L}^2 \text{T}^{-1} \] This is the same as the dimensional formula of Planck’s constant. - Linear momentum has the dimensional formula of: \[ [p] = \text{M L T}^{-1} \] This is different from the dimensional formula of Planck’s constant. - Force has the dimensional formula of: \[ [F] = \text{M L T}^{-2} \] This is also different from Planck's constant. - Velocity has the dimensional formula of: \[ [v] = \text{L T}^{-1} \] This is different from Planck’s constant. Therefore, the correct answer is Angular momentum because its dimensional formula is the same as Planck’s constant.