A rope is attached at one end to a fixed vertical pole . It is stretched horizontal with a fixed value of tension `T` . Suppose at `t=0`, a pulse is generated by moving the free end of the rope up and down once with your hand. The pulse arrives at the pole at instant `t`.
Ignoring the effect of gravity, answer the following quetions.
If you use a string of same length but of greater mass

Options

A. Time taken for the pulse to reach the pole will not change
B. Time taken for the pulse to reach the pole will increase
C. Time taken for the pulse to reach the pole will deacrease
D. Time taken for the pulse to reach the pole may increase or decrease

Explanation

To solve the problem, we need to analyze how the mass of the string affects the speed of the wave and consequently the time taken for the pulse to reach the pole.

### Step-by-Step Solution:

1. **Understanding Wave Speed**:
The speed of a wave (V) on a string is given by the formula:
\[ V = \sqrt{\frac{T}{\mu}} \]
where \(T\) is the tension in the string and \(\mu\) is the linear mass density (mass per unit length) of the string.

2. **Effect of Increased Mass**:
If we use a string of the same length but of greater mass, the linear mass density \(\mu\) will increase. This is because:
\[ \mu = \frac{m}{L} \]
where \(m\) is the mass of the string and \(L\) is its length. If the mass increases while the length remains constant, \(\mu\) increases.

3. **Calculating New Wave Speed**:
Since \(\mu\) increases, the wave speed \(V\) will decrease:
\[ V = \sqrt{\frac{T}{\mu}} \quad \text{(with increased } \mu\text{)} \]
This means that the wave will travel slower in the heavier string.

4. **Time Calculation**:
The time \(t\) taken for the pulse to reach the pole can be calculated using the formula:
\[ t = \frac{L}{V} \]
where \(L\) is the length of the string. Since \(L\) is constant and \(V\) has decreased due to the increased mass, the time \(t\) will increase.

5. **Conclusion**:
Therefore, the time taken for the pulse to reach the pole will increase when using a string of greater mass while keeping the length constant.

### Final Answer:
The time taken for the pulse to reach the pole will **increase**.