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 $mm$) upto which it can continue to float is (surface tension of water is $T=70\times {10}^{-3}N{m}^{-1}$)

• A. $1.5$
• B. $1.1$
• C. $0.75$
• D. $0.55$

Answer 1

Answer: (A)

$1.5$

specific gravity = $\frac{{\rho }_m}{{\rho }_w}$=8

so, ${\rho }_m=8{\rho }_w=8\left(1000\right)=8000kg/m^3$

To float,

$T\times 2\times L+{\rho }_w\left(AL\right)g={\rho }_m\left(AL\right)g$

$2T+{\rho }_w\pi (\frac{d}{2}{)}^{2}g={\rho }_m\pi (\frac{d}{2}{)}^{2}g$

$70\times {10}^{-3}\times 2+1000\pi \frac{d^2}{4}\times 10=8000\pi \frac{d^2}{4}\times 10$

(since specific gravity = $8$)

$70\times {10}^{-3}\times 2=7000\pi \frac{d^2}{4}\times 10$

$d\approx 1.5mm$