Question

A metal wire of density 'p' floats on water surface horizontally. If it is NOT to sink in water then maximum radius of wire is proportional to ______.

(T = surface tension of water, g = gravitational acceleration) 

विकल्प

• `sqrt ("T"/(pi"pg"))`

• `sqrt ((pi"pg")/"T")`

• ` "T"/(pi"pg")`

• `(pi"pg")/"T"`

Answer 1

A metal wire of density 'p' floats on water surface horizontally. If it is NOT to sink in water then maximum radius of wire is proportional to `sqrt ("T"/(pi"pg"))`.

Explanation:

For wire to float into water, its weight should be balanced by the surface tension of the water.

∴ mg = Tl  ....(where, I = length of the wire)

∴  Vpg = TI

∴ `pi^2` lpg = Tl

∴ `"r"^2 = "T"/(pi"pg")`

∴ `"r" =sqrt( "T"/(pi"pg"))`