A cylindrical wire of length 0.1m 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 0.07N/m. (Take g=10m/s2)
A
0.7mm
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B
0.711mm
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C
1411mm
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D
0.83mm
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Solution
The correct option is C1411mm
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=0.2m
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=
⎷0.07×4×2227×10×11000⇒d=1411×10−3m⇒d=1411mm