A metal wire of density rho floats on the wat | vedclass

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Question

(C) The correct option is $C$.For a wire of length $L$ and radius $r$ floating on the water surface,the downward force due to gravity is $F_g = mg = (

Vedclass · Accepted Answer

$\sqrt{\frac{2T}{\pi \rho g}}$

Vedclass · Answer

(C) The correct option is $C$.For a wire of length $L$ and radius $r$ floating on the water surface,the downward force due to gravity is $F_g = mg = (	ext{density} 	imes 	ext{volume}) 	imes g = ho (\pi r^2 L) g$.The upward force due to surface tension acts along the two sides of the wire along its length $L$. Thus,the total upward force is $F_T = 2TL$.For the wire to float without sinking,the upward force must balance the downward force:$2TL = ho \pi r^2 L g$$2T = ho \pi r^2 g$$r^2 = \frac{2T}{\pi ho g}$$r = \sqrt{\frac{2T}{\pi ho g}}$We neglect the buoyancy force as it is negligible compared to the surface tension force for a thin wire.

$A$ metal wire of density $\rho$ floats on the water surface horizontally. If it is not to sink in water,then the maximum radius of the wire is ($T$ = surface tension of water,$g$ = gravitational acceleration).

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