Correct Answer - Option 4 : Angular momentum
Concept:
-
Planck's Constant (h): Light is said to be made up of small particles with zero rest mass known as photon. The energy of such photon is related with its frequency by Planck's constant.
E = h ν
E is energy, ν is the frequency of the photon.
-
Dimensional Formula: It depicts the way to relate any unit to fundamental Units.
- If we have to find The dimensional formula of any quantity, At first, we find its units in terms of these fundamental units, and then replace units with these dimensions.
-
Angular Momentum: The angular momentum of a body of mass m moving with speed v with radius of circular path r is
L = m v r
- The dimensional formula for angular momentum will be
(Dimension of mass)(Dimension of speed)(Dimension of radius) = M L T -1 L = M L 2 T -1
Explanation:
Planck's constant can be given as
\(h = \frac{E}{\nu}\)
The Dimensional Formula of Energy is M L 2 T - 2
The dimension of Frequency is T - 1
The dimension of Planck's constant hence
\(H = \frac{ML^2 T^{-2}}{T^{-1}}\)
⇒ H = M L 2 T -1
This the dimension of angular momentum.
So, angular momentum is the correct option.
- Dimensional formula for Energy can be found using any expression for energy, for example, the expression for kinetic energy \(K = \frac{1}{2} mv^{2}\)
- Similarly, the dimensional formula of frequency can be obtained by relating it to the time period \(f = \frac{1}{T}\)
- Similarly, the dimensional formula for any units can be obtained.
| Fundamental Units |
Dimensions |
| Mass |
M |
| Length |
L |
| Time |
T |
| Temperature |
K |
| Current |
A |
