Statement I: two waves moving in a uniform string having uniform tension cannot have different velocities.
Elastic and inertial properties of string are same for all waves in same string. Moreover speed of wave in a string depends on its elastic and inertial properties only.

Options

A. Statement I is true, statement II is true and statement II is the correct explaination for statement I.
B. Statement I is true, statement II is true and statement II is NOT the correct explaination for statement I.
C. Statement I is true, statement II is false.
D. Statement I is false, statement II is true.

Explanation

To analyze the given statements, let's break them down step by step:

### Step 1: Understanding Wave Velocity in a String
The velocity of a wave traveling through a string can be expressed with the formula:
\[ v = \sqrt{\frac{T}{\mu}} \]
where:
- \( v \) is the wave velocity,
- \( T \) is the tension in the string,
- \( \mu \) is the mass per unit length of the string.

### Step 2: Analyzing Statement I
The first statement claims that "two waves moving in a uniform string having uniform tension cannot have different velocities."

- Since the string is uniform, it implies that both the tension \( T \) and the mass per unit length \( \mu \) are constant throughout the string.
- Given that both \( T \) and \( \mu \) are the same for both waves, the velocity \( v \) must also be the same according to the formula.

Thus, **Statement I is true**.

### Step 3: Analyzing Statement II
The second statement claims that "elastic and inertial properties of the string are the same for all the waves in the same string. Moreover, speed of wave in the string depends on its elastic and inertial properties only."

- The elastic properties refer to how the string responds to tension, while the inertial properties refer to the mass distribution (mass per unit length).
- Since the string is uniform, these properties are indeed the same for all waves traveling through it.
- The speed of the wave depends solely on these properties, confirming that the statement is correct.

Thus, **Statement II is also true**.

### Conclusion
Both statements are correct, and Statement II provides a correct explanation for Statement I.

### Final Answer:
Both statements are correct, and Statement II is the correct explanation of Statement I.

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