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Question

A cylindrical wire of length 0.1 m has specific gravity 11. What is the maximum diameter of the wire that can float on the surface of water, if surface tension of water is 0.07 N/m. (Take g=10 m/s2)

A
0.7 mm
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B
0.711 mm
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C
1411 mm
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D
0.83 mm
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Solution

The correct option is C 1411 mm

We know,
Mass = Volume × density
Mass of wire =π×(d2)2×l×11×103

Length of wire on which surface tension force is acting =2×l
L=2×l=(2×0.1) m=0.2 m

Now, we know,
T=FL
F=T×L=T×(2l)
As wire floats on the surface of water,
Weight of the wire (mg)= Surface tension force (F)
π×(d2)2×l×11000×10=T×(2l)d=  0.07×4×2227×10×11000d=1411×103 md=1411 mm

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