A soap film of surface tension `3 xx10^(-2) Nm^(-1)` formed in rectangular frame, can support a straw. The length of the film is 10 cm. Mass of the straw the film can support is

Options

A. 0.06 g
B. 0.6 g
C. 6 g
D. 60 g

Explanation

To find the mass of the straw that the soap film can support, we can use the concept of surface tension. The force exerted by the surface tension of the soap film can be calculated using the formula:

\[ F = \text{T} \times L \]

where:
- \( F \) is the force exerted by the surface tension,
- \( \text{T} \) is the surface tension of the soap film,
- \( L \) is the length of the film.

1. **Identify the given values:**
- Surface tension, \( \text{T} = 3 \times 10^{-2} \, \text{N/m} \)
- Length of the film, \( L = 10 \, \text{cm} = 0.1 \, \text{m} \)

2. **Calculate the force exerted by the surface tension:**
\[ F = \text{T} \times L = (3 \times 10^{-2} \, \text{N/m}) \times (0.1 \, \text{m}) \]
\[ F = 3 \times 10^{-3} \, \text{N} \]

3. **Relate the force to the weight of the straw:**
The force exerted by the surface tension must balance the weight of the straw, which can be expressed as:
\[ F = m \times g \]
where:
- \( m \) is the mass of the straw,
- \( g \) is the acceleration due to gravity (approximately \( 9.81 \, \text{m/s}^2 \)).

4. **Rearrange the equation to solve for mass \( m \):**
\[ m = \frac{F}{g} = \frac{3 \times 10^{-3} \, \text{N}}{9.81 \, \text{m/s}^2} \]

5. **Calculate the mass:**
\[ m \approx \frac{3 \times 10^{-3}}{9.81} \approx 3.06 \times 10^{-4} \, \text{kg} \]

6. **Convert the mass to grams:**
\[ m \approx 3.06 \times 10^{-4} \, \text{kg} \times 1000 \, \text{g/kg} \approx 0.306 \, \text{g} \]

Therefore, the mass of the straw that the soap film can support is approximately **0.306 grams**.