First slide

Surface tension

Question

A needle is made of a material whose density is $σ$ . Then the maximum diameter of the needle which can float on the surface of water with its length horizontal is, (surface tension of water is T)

Moderate

Solution

When the diametre of the needle is maximum, half of its volume is submerged.
$∴$ In equilibriums $l T + l T = σ . \frac{π d_{m a x}^{2}}{4} . l . g$
$\Rightarrow d_{m a x} = \sqrt{\frac{4 T}{π σ g}}$

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