A glass tube of internal diameter 3.5cm and thickness 0.5 cm is held vertically with its lower end immersed in water . The downward pull on the tube to surface tension (S.T.of water =0.074N//m) is

Options

A. `1.86xx10^(-2)`N
B. `1.86xx10^(-3)` N
C. `1.86xx10^(-1)` N
D. 1.86 N

Answer

To find the downward pull on the glass tube due to surface tension, we will follow these steps:

### Step 1: Identify the internal and external diameters
Given:
- Internal diameter (d) = 3.5 cm
- Thickness of the tube (t) = 0.5 cm

**Calculation of internal and external radii:**
- Internal radius (r) = d/2 = 3.5 cm / 2 = 1.75 cm
- External diameter = Internal diameter + 2 * Thickness = 3.5 cm + 2 * 0.5 cm = 4.5 cm
- External radius (R) = External diameter / 2 = 4.5 cm / 2 = 2.25 cm

### Step 2: Convert the radii to meters
- Internal radius (r) = 1.75 cm = 1.75 * 10^-2 m
- External radius (R) = 2.25 cm = 2.25 * 10^-2 m

### Step 3: Calculate the force due to surface tension
The force due to surface tension (F) is given by the formula:
\[ F = S.T \times L \]
where \( S.T \) is the surface tension and \( L \) is the length of the circumference.

**Circumference for internal and external surfaces:**
- Internal circumference = 2πr
- External circumference = 2πR

### Step 4: Calculate the total force due to surface tension
The total downward pull (F_total) on the tube is the sum of the forces due to the internal and external surfaces:
\[ F_{total} = S.T \times (2\pi R + 2\pi r) \]
\[ F_{total} = S.T \times 2\pi(R + r) \]

### Step 5: Substitute the values
Given:
- Surface tension (S.T) = 0.074 N/m

Substituting the values:
\[ F_{total} = 0.074 \times 2\pi \times (2.25 \times 10^{-2} + 1.75 \times 10^{-2}) \]
\[ F_{total} = 0.074 \times 2\pi \times (4.00 \times 10^{-2}) \]

### Step 6: Calculate the numerical value
Now, calculating the numerical value:
\[ F_{total} = 0.074 \times 2\pi \times 0.04 \]
\[ F_{total} = 0.074 \times 0.2513 \]
\[ F_{total} \approx 0.0186 \, \text{N} \]

### Final Answer:
The downward pull on the tube due to surface tension is approximately **0.0186 N**.

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