A 10 m long steel wire has mass 5 g. If the wire is under a tension of 80 N, the speed of transverse waves on the wire is

Options

A. `100ms^(-1)`
B. `200ms^(-1)`
C. `400ms^(-1)`
D. `500ms^(-1)`

Explanation

To find the speed of transverse waves on a steel wire, we can use the formula:

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

where:
- \( V \) is the speed of the wave,
- \( T \) is the tension in the wire,
- \( \mu \) is the mass per unit length of the wire.

### Step 1: Convert mass from grams to kilograms
The mass of the wire is given as 5 grams. We need to convert this to kilograms because the SI unit of mass is kilograms.

\[ \text{Mass in kg} = \frac{5 \text{ g}}{1000} = 0.005 \text{ kg} \]

### Step 2: Calculate the mass per unit length (\( \mu \))
The length of the wire is given as 10 meters. The mass per unit length (\( \mu \)) can be calculated using the formula:

\[ \mu = \frac{\text{mass}}{\text{length}} = \frac{0.005 \text{ kg}}{10 \text{ m}} = 0.0005 \text{ kg/m} \]

### Step 3: Substitute the values into the wave speed formula
Now we can substitute the values of tension (\( T = 80 \text{ N} \)) and mass per unit length (\( \mu = 0.0005 \text{ kg/m} \)) into the wave speed formula:

\[ V = \sqrt{\frac{T}{\mu}} = \sqrt{\frac{80 \text{ N}}{0.0005 \text{ kg/m}}} \]

### Step 4: Calculate the value inside the square root
First, we calculate \( \frac{80}{0.0005} \):

\[ \frac{80}{0.0005} = 160000 \]

### Step 5: Take the square root
Now we take the square root of 160000:

\[ V = \sqrt{160000} = 400 \text{ m/s} \]

### Conclusion
The speed of transverse waves on the wire is \( 400 \text{ m/s} \).