Question

A wire of length l metre, 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 millimetre) upto which it can continue to float is (surface tension of water bit $T=70\times {10}^{-3}N{m}^{-1}$) :

• A. 1.5
• B. 1.1
• C. 0.75
• D. 0.55

Answer 1

The correct option is B 1.1

We have
$T\cdot I=V_{\rho }g$
or $T\cdot I=\pi r^2\rho g$
or $T=\pi r^2\rho g$
$\therefore 70\times {10}^{-3}=314\times r^2\times 8\times {10}^{-3}\times 9.8$or $r^2=\frac{70\times {10}^{-3}}{314\times 8\times {10}^{-3}\times 9.8}$
$r^2=0.28$
$\therefore r=0.53$
$\therefore$ Minimum diameter of the wire $=2r$
$=2\times 0.53\approx 1.1m$