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A wire of length 'I' 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 millimeters) upto which it can continue to float is (surface tension of water is $T = 70 \times 10^{- 3} {Nm}^{- 1}$ )

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0.75

0.55

1.1

1.5

answer is A.

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Detailed Solution

Given,

Specific gravity,

$\frac{ρ_{m}}{ρ_{w}} = 8 \Rightarrow ρ_{m} = 8 ρ_{w} = 8 \times 1000 = 8000 kg / m^{3}$

to float,

$T \times 2 \times L + ρ_{w} (AL) g = ρ_{m} (AL) g$

$2 T = ρ_{w} π {(\frac{d}{2})}^{2} g = ρ_{m} π {(\frac{d}{2})}^{2} g$

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

$d = 1.5 mm$

Hence the correct answer is 1.5.

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