Question

The dimensions of Planck’s constant are same as the product of

• A. time and displacement
• B. force and time
• C. force, displacement and time
• D. force and displacement

Hint:

Planck’s constant represents action, which has dimensions of angular momentum.

Answer 1

The Correct Option is C

Step 1: Write dimensional formula of Planck’s constant.
Planck’s constant has dimensions of angular momentum or action.
\[ [h] = [E][T] = (ML^2T^{-2})T = ML^2T^{-1} \]

Step 2: Write dimensions of force, displacement and time.
\[ [\text{Force}] = MLT^{-2} \] \[ [\text{Displacement}] = L \] \[ [\text{Time}] = T \]

Step 3: Multiply dimensions.
\[ (MLT^{-2})(L)(T) = ML^2T^{-1} \]

Step 4: Conclusion.
Thus, Planck’s constant has the same dimensions as the product of force, displacement and time.