Choose the correct statement.

Options

A. The diamension of `(omegaL)/(R)` are same as that of strain
B. The diamensions of `(1)/(sqrtLC)` are same as that of angular velocity
C. The dimension of LCR are same as that of time
D. none of the above

Answer

To solve the question regarding the correct statements about the dimensions of various quantities in the context of alternating current, we will analyze the statements step by step.

### Step 1: Understanding the dimensions of inductive reactance and resistance
Inductive reactance (X_L) is given by the formula:
\[ X_L = \omega L \]
where:
- \( \omega \) is the angular frequency (in radians per second) with dimensions of \( [T^{-1}] \),
- \( L \) is the inductance (in henries) with dimensions of \( [M L^2 T^{-2}] \).

Resistance (R) has dimensions of:
\[ [M L^2 T^{-3} I^{-2}] \]

### Step 2: Finding the dimensions of \( \frac{\omega L}{R} \)
To find the dimensions of \( \frac{\omega L}{R} \):
1. The dimensions of \( \omega L \):
\[ [\omega L] = [T^{-1}] \cdot [M L^2 T^{-2}] = [M L^2 T^{-3}] \]

2. The dimensions of \( R \):
\[ [R] = [M L^2 T^{-3} I^{-2}] \]

3. Now, calculate \( \frac{\omega L}{R} \):
\[ \frac{\omega L}{R} = \frac{[M L^2 T^{-3}]}{[M L^2 T^{-3} I^{-2}]} = [I^2] \]

### Step 3: Analyzing the dimensions of \( \frac{1}{\sqrt{LC}} \)
The dimensions of \( C \) (capacitance) are:
\[ [C] = [M^{-1} L^{-2} T^4 I^2] \]

1. The dimensions of \( L \) are already calculated as \( [M L^2 T^{-2}] \).
2. Now calculate \( LC \):
\[ [LC] = [M L^2 T^{-2}] \cdot [M^{-1} L^{-2} T^4 I^2] = [T^2 I^2] \]

3. Therefore, the dimensions of \( \frac{1}{\sqrt{LC}} \):
\[ \frac{1}{\sqrt{LC}} = [T^{-1} I^{-1}] \]

### Step 4: Comparing with angular velocity
Angular velocity \( \omega \) has dimensions of:
\[ [T^{-1}] \]

### Conclusion
From the analysis:
- The dimension of \( \frac{\omega L}{R} \) is \( [I^2] \).
- The dimension of \( \frac{1}{\sqrt{LC}} \) is \( [T^{-1} I^{-1}] \), which is the same as the dimension of angular frequency \( \omega \).

Thus, both statements regarding the dimensions are correct.

### Final Answer
Both Option 1 and Option 2 are correct.