Question

A ring is cut from a platinum tube $8.5cm$ internal and $8.7cm$ external diameter. It is supported horizontally from the pan of a balance, so that it comes in contact with the water in a glass vessel. If an extra $3.103gf$ is required to pull it away from water, the surface tension of water is:

• A. $56.27$ dyne/cm
• B. $70.80$ dyne/cm
• C. $63.35$ dyne/cm
• D. $60$ dyne/cm

Answer 1

The correct option is A $56.27$ dyne/cm

Total force on the ring due to surface tension is given by $F=T(2\pi r_1+2\pi r_2)$, where $T$ is surface tension of water, and $r_1$ and $r_2$ are inner and outer radii of the ring.
$\Rightarrow T=\frac{F}{\pi (2r_1+2r_2)}$
$\Rightarrow T=\frac{3.103\times 980}{\pi (8.5+8.7)}\because$ excess weight is compensated by surface tension force
$\Rightarrow T=\frac{3.103\times 980}{\left(\frac{22}{7}\right)\times 17.2}=56.2768\text{dyne/cm}$