What is the radius of the biggest aluminium coin of thickness t and density ρ , which will be able to float on the water surface of surface tension T ? ( g = acceleration due to gravity)

Question

TestHub · Accepted Answer

For the coin to float on the water surface, the maximum upward force due to surface tension must balance the downward weight of the coin.

The maximum upward force due to surface tension acts along the perimeter of the coin:
$F = T \times 2 π r$

The weight of the coin is:
$W = m g = (π r^{2} t) ρ g$

Equating the upward surface tension force and the downward weight:
$T \times 2 π r = π r^{2} tρ g$

$2 T = r tρ g$

$r = \frac{2 T}{ρ g t}$

Answer: $\frac{2 T}{ρ g t}$

Physics - Fluid Question with Solution | TestHub

Options:

Doubts & Discussion