Force necessary to pull a circular plate of 5cm radius from water surface for which surface tension is 75 dynes/cm, is

To find the force necessary to pull a circular plate from the water surface, we need to consider the force exerted by the surface tension of the liquid along the boundary of contact.

Surface tension ($T$) is defined as the force per unit length acting perpendicular to any line on the liquid surface. When a circular plate of radius $r$ is lifted from the water surface, the water clings to the boundary of the plate. Therefore, the total length ($L$) of the line of contact where surface tension acts is the circumference of the circular plate:

$L=2\pi r$

The upward force ($F$) required to overcome this surface tension is given by the formula:

$F=T\times L$

Substituting the expression for the circumference, we get:

$F=T\times 2\pi r$

Now, let's identify the given values from the problem:
Radius of the plate, $r=5\text{cm}$
Surface tension of water, $T=75\text{dynes/cm}$

Substitute these values into the force equation:

$F=75\times 2\times \pi \times 5$

Simplify the expression:

$F=750\pi \text{dynes}$

Therefore, the force necessary to pull the circular plate from the water surface is 750 π dynes.