A rope of length 20 cm is kept on frictionless surface and a force of 5 N is applied to one of its end. Find the tension in the rope at 5m from this end.

Options

A. 5 N
B. 2 N
C. 3.75 N
D. 4 N

Explanation

To find the tension in the rope at a distance of 5 cm from the end where a force of 5 N is applied, we can use the formula for tension in a rope under a uniform force.

### Step-by-step Solution:

1. **Identify Given Values**:
- Length of the rope (L) = 20 cm = 0.2 m
- Force applied (F) = 5 N
- Distance from the end where tension is to be calculated (X) = 5 cm = 0.05 m

2. **Use the Tension Formula**:
The formula for tension (T) at a distance X from the end of the rope is given by:
\[ T = F \times \frac{L - X}{L} \]

3. **Substitute the Values**:
Substitute the known values into the formula:
\[ T = 5 \, \text{N} \times \frac{20 \, \text{cm} - 5 \, \text{cm}}{20 \, \text{cm}} \]
\[ T = 5 \, \text{N} \times \frac{15 \, \text{cm}}{20 \, \text{cm}} \]

4. **Simplify the Calculation**:
\[ T = 5 \, \text{N} \times \frac{15}{20} \]
\[ T = 5 \, \text{N} \times \frac{3}{4} \]
\[ T = 5 \times 0.75 = 3.75 \, \text{N} \]

5. **Final Answer**:
The tension in the rope at 5 cm from the end where the force is applied is **3.75 N**.