1. Use viscous force formula for a liquid film

When a block moves over a table with a thin liquid film of thickness $d$ between them, the viscous force is

$F = \eta A \frac{v}{d}$

where:

• $F = 0.1\,\text{N}$
• $A = 0.20\,\text{m}^2$
• $d = 0.25\,\text{mm} = 2.5\times 10^{-4}\,\text{m}$
• $\eta = 5.0\times 10^{-3}\,\text{Pl}$

2. Convert poise to SI unit

Since

$1\,\text{poise} = 0.1\,\text{Pa·s}$

therefore,

$\eta = 5.0\times 10^{-3}\,\text{Pl} = 5.0\times 10^{-4}\,\text{Pa·s}$

3. At constant speed, applied force equals viscous drag

So,

$0.1 = \eta A \frac{v}{d}$

Substitute values:

$0.1 = \left(5.0\times 10^{-4}\right)(0.20)\frac{v}{2.5\times 10^{-4}}$

4. Solve for $v$

First compute:

$\eta A = 5.0\times 10^{-4} \times 0.20 = 1.0\times 10^{-4}$

Hence,

$0.1 = 1.0\times 10^{-4}\cdot \frac{v}{2.5\times 10^{-4}}$

$0.1 = \frac{1.0}{2.5}v = 0.4v$

So,

$v = \frac{0.1}{0.4} = 0.25\,\text{m/s}$

5. Express in the required form

We need

$v = \underline{\hspace{1cm}}\times 10^{-3}\,\text{m/s}$

Since

$0.25\,\text{m/s} = 250\times 10^{-3}\,\text{m/s}$

So the required integer is:

$\boxed{250}$

6. Comparison with stored answer

Stored correct answer is $25$, but the correct calculated value is $250$.

It appears the stored answer may have arisen from an error in unit conversion or decimal placement.