The mass of a 10 m long wire is 100 grams. If a tension of 100 N is applied, calculate the time taken by a transverse wave to travel from one end to the other end of the wire.

Options

A. 0.5s
B. 0.1s
C. 2s
D. 2.5s

Answer

To solve the problem of calculating the time taken by a transverse wave to travel from one end to the other end of a wire, we can follow these steps:

### Step 1: Convert the mass of the wire to kilograms
Given that the mass of the wire is 100 grams, we need to convert this to kilograms for consistency in SI units.

\[ \text{Mass} = 100 \text{ grams} = 0.1 \text{ kg} \]

### Step 2: Identify the length of the wire
The length of the wire is given as:

\[ L = 10 \text{ m} \]

### Step 3: Identify the tension in the wire
The tension applied to the wire is given as:

\[ T = 100 \text{ N} \]

### Step 4: Calculate the mass per unit length (μ)
The mass per unit length (μ) is calculated using the formula:

\[ \mu = \frac{\text{mass}}{\text{length}} = \frac{0.1 \text{ kg}}{10 \text{ m}} = 0.01 \text{ kg/m} \]

### Step 5: Calculate the wave velocity (v)
The velocity of the transverse wave in the wire can be calculated using the formula:

\[ v = \sqrt{\frac{T}{\mu}} \]

Substituting the values of tension (T) and mass per unit length (μ):

\[ v = \sqrt{\frac{100 \text{ N}}{0.01 \text{ kg/m}}} = \sqrt{10000} = 100 \text{ m/s} \]

### Step 6: Calculate the time taken (t) for the wave to travel the length of the wire
The time taken for the wave to travel from one end to the other is given by:

\[ t = \frac{L}{v} \]

Substituting the values of length (L) and velocity (v):

\[ t = \frac{10 \text{ m}}{100 \text{ m/s}} = 0.1 \text{ seconds} \]

### Final Answer
The time taken by the transverse wave to travel from one end to the other end of the wire is:

\[ \boxed{0.1 \text{ seconds}} \]