Question:
A metallic wire of density $\rho$ is placed horizontally on the surface of a liquid with surface tension $T$. What is the maximum radius the wire can have so that it remains supported by surface tension?
A metallic wire of density $\rho$ is placed horizontally on the surface of a liquid with surface tension $T$. What is the maximum radius the wire can have so that it remains supported by surface tension?
Show Hint
Remember that surface tension acts on both sides of the wire length, effectively doubling the supporting force to $2TL$.
Updated On: Jun 6, 2026
- $\sqrt{\frac{2T}{\pi \rho g}}$
- $\sqrt{\frac{T}{\pi \rho g}}$
- $\sqrt{\frac{3 \rho g}{2T}}$
- $\sqrt{\frac{2 \pi}{T \rho g}}$
Show Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
Step 1: Concept
The wire is supported if the upward force due to surface tension balances the downward weight of the wire.
Step 2: Meaning
For a long wire of length $L$ and radius $r$, the weight $W = mg = (\text{Volume} \times \rho) \times g = (\pi r^2 L) \rho g$. The upward force due to surface tension acts along both sides of the wire, so $F = 2 \times (T \times L) = 2TL$.
Step 3: Analysis
Equating the forces: $2TL = (\pi r^2 L) \rho g$. The length $L$ cancels out: $2T = \pi r^2 \rho g$. Solving for $r^2$: $r^2 = \frac{2T}{\pi \rho g}$. Taking the square root: $r = \sqrt{\frac{2T}{\pi \rho g}}$.
Step 4: Conclusion
The maximum radius $r$ for which the wire is supported is $\sqrt{\frac{2T}{\pi \rho g}}$.
Final Answer: (A)
The wire is supported if the upward force due to surface tension balances the downward weight of the wire.
Step 2: Meaning
For a long wire of length $L$ and radius $r$, the weight $W = mg = (\text{Volume} \times \rho) \times g = (\pi r^2 L) \rho g$. The upward force due to surface tension acts along both sides of the wire, so $F = 2 \times (T \times L) = 2TL$.
Step 3: Analysis
Equating the forces: $2TL = (\pi r^2 L) \rho g$. The length $L$ cancels out: $2T = \pi r^2 \rho g$. Solving for $r^2$: $r^2 = \frac{2T}{\pi \rho g}$. Taking the square root: $r = \sqrt{\frac{2T}{\pi \rho g}}$.
Step 4: Conclusion
The maximum radius $r$ for which the wire is supported is $\sqrt{\frac{2T}{\pi \rho g}}$.
Final Answer: (A)
Was this answer helpful?
0
0
Top AP EAPCET Physics Questions
- A body is projected from the ground at an angle of $\tan^{-1} \left( \frac{8}{7}\right)$ with the horizontal. The ratio of the maximum height attained by it to its range is
- A lens forms real and virtual images of an object, when the object is at $u_{1}$ and $u_{2}$ distances respectively. If the size of the virtual image is double that of the real image, then the focal length of the lens is (take, the magnification of the real image as $m$ )
- Two spheres $P$ and $Q$, each of mass $200\, g$ are attached to a string of length one metre as shown in the figure. The string and the spheres are then whirled in a horizontal circle about $O$ at a constant angular speed. The ratio of the tension in the string between $P$ and $Q$ to that of between $P$ and $O$ is $(P$ is at mid-point of the line joining $O$ and $Q$ )
- The radii of the two columns in a U - tube are r1 and r2. When a liquid of density p (angle of contact is $ 0{}^\circ $ ) is filled in it, the level difference of the liquid in the two arms is h. The surface tension of the liquid is: (g = acceleration due to gravity)
- A rigid metallic sphere is spinning around its own axis in the absence of external torque. If the temperature is raised, its volume increases by $9 \%$. The change in its angular speed is
View More Questions
Top AP EAPCET mechanical properties of fluid Questions
- A soap bubble of radius $1$ cm has surface tension $0.03$ N/m. Excess pressure inside is:
- A liquid rises to a height of $4 \text{ cm}$ in a capillary tube of radius $r$. If another capillary tube of radius $r/2$ is dipped in the same liquid, the height of liquid rise will be
- The rate of flow of a liquid through a capillary tube of radius $r$ and length $l$ under a pressure difference $P$ is proportional to
- Calculate the amount of work done in spraying a drop of a liquid of radius 1 mm into million identical droplets under isothermal conditions. [surface tension of liquid $=550\times10^{-3}\text{Nm}^{-1}$]
- A long cylindrical vessel of glass having a hole of 0.5 mm radius at its bottom is slowly lowered vertically into a deep water bath. If the surface tension of water is \( 7 \times 10^{-2} \, Nm^{-1} \) then the maximum depth the vessel can be submerged without water entering through the hole is: (Acceleration due to gravity \( = 10 \, ms^{-2} \))
View More Questions
Top AP EAPCET Questions
- A body is projected from the ground at an angle of $\tan^{-1} \left( \frac{8}{7}\right)$ with the horizontal. The ratio of the maximum height attained by it to its range is
- The four quantum numbers of the valence electron of potassium are :
- A lens forms real and virtual images of an object, when the object is at $u_{1}$ and $u_{2}$ distances respectively. If the size of the virtual image is double that of the real image, then the focal length of the lens is (take, the magnification of the real image as $m$ )
- Two spheres $P$ and $Q$, each of mass $200\, g$ are attached to a string of length one metre as shown in the figure. The string and the spheres are then whirled in a horizontal circle about $O$ at a constant angular speed. The ratio of the tension in the string between $P$ and $Q$ to that of between $P$ and $O$ is $(P$ is at mid-point of the line joining $O$ and $Q$ )
- The volume of $0.02\, M$ acidified permanganate solution required for complete reaction of $60\, mL$ of $0.01\, MI^{-}$ ion solution to form $I_2$ in $mL$ is
View More Questions