Question

The force required to take away a flat plate of radius $4\mathrm{cm}$ from the surface of the water is (surface tension of water $=70\mathrm{dyne}/\mathrm{cm}$)?

Answer 1

Step 1: Given data:

The radius of the flat plate is given as $\left(\mathrm{r}\right)=$ $4\mathrm{cm}$

The surface tension of water is given as $=70\mathrm{dyne}/\mathrm{cm}$

Step 2: Formula for calculating Force required:

We know the surface tension formula is given as:

$\mathrm{Surface}\mathrm{tension}\left(\mathrm{T}\right)=\frac{\mathrm{Force}\left(\mathrm{F}\right)}{\mathrm{Length}}$

As the force due to surface tension acts all along the circumference of the circular plate.

The length can be given as:

length = circumference of the circular plate $=2\mathrm{\pi r}$

Hence, the formula for Force required can be given as:

$\mathrm{Force}\left(\mathrm{F}\right)=\mathrm{T}\mathrm{x}2\mathrm{\pi r}$

Step 3: Calculating Force required to take away of plate:

Thus, putting the values given, the force required to take away of the plate can be given as:

$$\begin{gathered} \mathrm{F}=\mathrm{T}\mathrm{x}2\mathrm{\pi r} \\ \mathrm{F}=70\mathrm{x}2\mathrm{x}3.14\mathrm{x}4 \\ =1758.4\mathrm{dyne}/\mathrm{cm} \end{gathered}$$

Hence, the force required to take away a flat plate of radius $4\mathrm{cm}$ from the surface of the water is $1758.4\mathrm{dyne}/\mathrm{cm}$