If the unit of tension is divided by the unit of surface tension the derived unit will be same as that of

Options

A. Mass
B. Length
C. Area
D. Work

Answer

To solve the problem, we need to analyze the units of tension and surface tension and then perform the division as described in the question.

### Step-by-Step Solution:

1. **Identify the Unit of Tension:**
- Tension is a force, and the SI unit of force is the Newton (N).
- The dimensional formula for force (and hence tension) is given by:
\[ [\text{Force}] = [\text{Mass}] \times [\text{Acceleration}] = \text{kg} \cdot \text{m/s}^2 \]
- In terms of base units, this can be expressed as:
\[ [\text{Tension}] = [\text{M}] [\text{L}] [\text{T}]^{-2} = \text{M} \text{L} \text{T}^{-2} \]

2. **Identify the Unit of Surface Tension:**
- Surface tension is defined as force per unit length.
- The unit of surface tension is therefore:
\[ [\text{Surface Tension}] = \frac{[\text{Force}]}{[\text{Length}]} = \frac{\text{N}}{\text{m}} = \frac{\text{kg} \cdot \text{m/s}^2}{\text{m}} = \text{kg/s}^2 \]
- In dimensional terms, this is:
\[ [\text{Surface Tension}] = \frac{[\text{M}] [\text{L}] [\text{T}]^{-2}}{[\text{L}]} = [\text{M}] [\text{T}]^{-2} \]

3. **Perform the Division of Units:**
- Now, we need to divide the unit of tension by the unit of surface tension:
\[ \text{Result} = \frac{[\text{Tension}]}{[\text{Surface Tension}]} = \frac{[\text{M}][\text{L}][\text{T}]^{-2}}{[\text{M}][\text{T}]^{-2}} \]
- Simplifying this gives:
\[ \text{Result} = \frac{[\text{M}][\text{L}][\text{T}]^{-2}}{[\text{M}][\text{T}]^{-2}} = [\text{L}] \]

4. **Conclusion:**
- The derived unit from dividing the unit of tension by the unit of surface tension is the unit of length (L).

### Final Answer:
The derived unit will be the same as that of **length (L)**.

---