Photon is quantum of radiation with energy E =hv where v is frequency and h is Planck's constant. The dimensions of h are the same as that of

Options

A. linear impulse
B. angular impulse
C. linear momentum
D. angular momentum

Explanation

To solve the problem, we need to find the dimensions of Planck's constant (h) and compare it with the dimensions of the given options.

### Step-by-Step Solution:

1. **Understand the relationship**: We start with the equation for the energy of a photon:
\[ E = h \nu \]
where \(E\) is energy, \(h\) is Planck's constant, and \(\nu\) is the frequency.

2. **Express dimensions**: We will express the dimensions of both sides of the equation. The dimensions of energy \(E\) can be expressed as:
\[ [E] = [\text{Force}] \times [\text{Displacement}] = [M L T^{-2}] \times [L] = [M L^2 T^{-2}] \]
where \(M\) is mass, \(L\) is length, and \(T\) is time.

3. **Frequency dimensions**: The frequency \(\nu\) is the reciprocal of time, so its dimensions are:
\[ [\nu] = [T^{-1}] \]

4. **Relate dimensions**: Now, substituting the dimensions into the equation \(E = h \nu\):
\[ [E] = [h] \times [\nu] \]
This gives us:
\[ [M L^2 T^{-2}] = [h] \times [T^{-1}] \]

5. **Solve for dimensions of Planck's constant**: Rearranging the equation to solve for the dimensions of \(h\):
\[ [h] = \frac{[M L^2 T^{-2}]}{[T^{-1}]} = [M L^2 T^{-1}] \]

6. **Compare with options**: Now we need to find the dimensions of the given options:
- **Option 1: Linear impulse**: The dimensional formula of linear impulse is the same as that of linear momentum:
\[ [\text{Linear Impulse}] = [M L T^{-1}] \]
- **Option 2: Angular impulse**: The dimensional formula of angular impulse is the same as that of angular momentum:
\[ [\text{Angular Impulse}] = [M L^2 T^{-1}] \]
- **Option 3: Linear momentum**: The dimensional formula of linear momentum is:
\[ [\text{Linear Momentum}] = [M L T^{-1}] \]
- **Option 4: Angular momentum**: The dimensional formula of angular momentum is:
\[ [\text{Angular Momentum}] = [M L^2 T^{-1}] \]

7. **Identify matching dimensions**: Now we compare the dimensions:
- The dimensions of Planck's constant \( [M L^2 T^{-1}] \) match with:
- Angular impulse (Option 2)
- Angular momentum (Option 4)

### Conclusion:
The dimensions of Planck's constant \(h\) are the same as those of angular impulse and angular momentum. Therefore, the correct options are **Option 2 and Option 4**.