Question

Dimension of Planck's constant is same as that of:

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

Hint:

The dimension of Planck's constant \( h \) is the same as the dimension of angular momentum, \( M L^2 T^{-1} \).

Answer 1

The Correct Option is C

The dimension of Planck's constant \( h \) can be derived from its relation to energy and frequency: \[ E = h \nu \] Where \( E \) is the energy, \( h \) is Planck's constant, and \( \nu \) is the frequency. The dimensions of energy are: \[ [E] = M L^2 T^{-2} \] And the dimensions of frequency are: \[ [\nu] = T^{-1} \] From the equation \( E = h \nu \), we get: \[ [h] = \frac{E}{\nu} = \frac{M L^2 T^{-2}}{T^{-1}} = M L^2 T^{-1} \] This is the same as the dimension of angular momentum, which is: \[ [L] = M L^2 T^{-1} \] Thus, the dimension of Planck's constant is the same as that of angular momentum.
Final Answer: (C) Angular momentum