Question

A thin metal ring of internal radius $8\text{cm}$ and external radius $9\text{cm}$ is supported horizontally from the pan of a balance so that it comes in contact with pure water in a glass vessel. If it is found that an extra weight of $7.48\text{g}$ is required to pull the ring out of pure water. The surface tension of water is
[Angle of contact of glass-pure water is $0^{\circ }$]

($g=10{\text{m/s}}^2$)

• A. $80\times {10}^{-3}\text{N/m}$
• B. $25\times {10}^{-3}\text{N/m}$
• C. $45\times {10}^{-3}\text{N/m}$
• D. $70\times {10}^{-3}\text{N/m}$

Answer 1

The correct option is D $70\times {10}^{-3}\text{N/m}$



The extra weight produced is due to the surface tension on both sides of the ring (inner and outer).
$\Rightarrow W=2\pi r_{1}T+2\pi r_{2}T[\because T=\frac{F}{L}]$

$\Rightarrow 7.48\times {10}^{-3}\times 10=2\times 3.14\times T\times (8\times {10}^{-2}+9\times {10}^{-2})$

$\Rightarrow T=\frac{7.48\times {10}^{-2}}{1.07}\approx 0.07\text{N/m}=70\times {10}^{-3}\text{N/m}$
So, the correct option is (d).