First slide

Surface tension

Question

A wire of length ‘l’ meters, made of a material of specific gravity 8 is floating horizontally on the surface of water. If it is not wet by water, the maximum diameter of the wire (in milli-meters) upto which it can continue to float is (surface tension of water is T = 70×10^–3 Nm^–1)

Moderate

A

1.5
B

1.1
C

0.75
D

0.55

Solution

$\large W=mg=\frac {\pi d^2_{max}}{4}.l.\sigma.g$
$\large \therefore\frac {\pi d^2_{max}}{4}l\sigma g=sl+sl$
$\large \Rightarrow d_{max}=\sqrt {\frac {8s}{\pi \sigma g}}$
Here, σ = density of wire = 8 x 10³ kg/m³ ; s = surface tension = 7 x 10^-2 N/m
$\large \therefore d_{max}=\sqrt {\frac {8\times 7\times 10^{-2}}{\pi \times 8\times 10^3\times 10}}=1.5\;mm$

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