A metal wire of length L and density d floats | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) For the wire to float, the downward force due to gravity must be balanced by the upward force due to surface tension and buoyancy.$1$. The weight

Vedclass · Accepted Answer

$\sqrt{\frac{2T}{\pi dg}}$

Vedclass · Answer

(A) For the wire to float, the downward force due to gravity must be balanced by the upward force due to surface tension and buoyancy.$1$. The weight of the wire is $W = mg = (	ext{Volume} 	imes 	ext{density}) 	imes g = (\pi r^2 L) d g$.$2$. The upward force due to surface tension acts along the two sides of the wire. The force is $F_s = 2 	imes (T 	imes L) = 2TL$.$3$. For the wire to just float, the weight must be equal to the surface tension force (ignoring buoyancy as the wire is thin and floating on the surface): $\pi r^2 L d g = 2TL$.$4$. Solving for $r$: $r^2 = \frac{2T}{\pi dg}$.$5$. Therefore, the maximum radius is $r = \sqrt{\frac{2T}{\pi dg}}$.

$A$ metal wire of length $L$ and density $d$ floats horizontally on the free surface of water. What is the maximum radius of the wire such that it does not sink in water? [$T$ = surface tension of water, $g$ = gravitational acceleration]

Similar Questions

The temperature at which the surface tension of water is zero is:

If a drop of liquid breaks into smaller droplets,it results in the lowering of the temperature of the droplets. Let a drop of radius $R$ break into $N$ small droplets,each of radius $r$. Estimate the drop in temperature.

Soap helps in cleaning clothes,because

It is easier to spray water to which soap is added because the addition of soap to water:

Figure $(a)$ shows a thin liquid film supporting a small weight $= 4.5 \times 10^{-2} \, N$. What is the weight supported by a film of the same liquid at the same temperature in Figure $(b)$ and $(c)$? Explain your answer physically.

Vedclass Test Series

Exam Paper Generator

Online Exam Module