Question

A ring is cut from a platinum tube having $8.5cm$ internal and $8.7cm$ external diameter. It is supported horizontally from a pair of a balance so that it comes in contact with the water in glass vessel. If an extra $3.97g$ weight is required to pull it away from water, the surface tension of water is

• A. $72.07dynec{m}^{-1}$
• B. $70.80dynec{m}^{-1}$
• C. $65.35dynec{m}^{-1}$
• D. $60.00dynec{m}^{-1}$

Answer 1

Answer: (A)

$72.07dynec{m}^{-1}$

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.
$\Rightarrow T=\frac{F}{\pi (2r_1+2r_2)}$
$\Rightarrow T=\frac{3.97\times 980}{\pi (8.5+8.7)}\because$ excess weight is compensated by surface tension force
$\Rightarrow T=\frac{3.97\times 980}{\left(\frac{22}{7}\right)\times 17.2}=72.00dyne/cm$