A wire of length '1' 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 = 70x10^-3 Nm^-1)

In a position where the wire is about to sink the water meniscus curves down, meeting the wire at 90°

So, upward tension force F, (meniscus against inner and outer ring) ..F = T x 2L

Apparent weight of ring in water, W(ap) = (ring weight in air - water upthrust)
Weight in air = 8x water weight of same volume
Water upthrust = 1/8 ring weight .. .. .. so W(ap) = 7x water weight of same volume
W(ap) = (πr²L)m³ x (7 x 1000)kg/m³ x 9.80N/kg

At equilibrium .. W(ap)↓ = 2TL↑
πr²L x (7 x 1000) x 9.80 = 2TL .. ..L cancels out

r² = 2(70^-3) / (π x 7000 x 9.80) = 6.50^-7 .. .. .. ►r =8.10^-4 m .. (0.80mm)