Find the maximum possible mass of a greased needle floating on water surface. T is the surface tension of water, is the length of the needle

Question

TestHub · Accepted Answer

To float, the needle's weight must be balanced by the surface tension force.

Weight of needle: $W = m_{ma x} g$

Force due to surface tension: $F_{T} = T \times (2 ℓ)$ (since there are two lengths of contact, one on each side of the needle)

Equate forces for equilibrium:

$m_{ma x} g = 2 T ℓ$

$m_{ma x} = \frac{2 T ℓ}{g}$

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