Question

The minimum velocity of capillary waves on the surface of water is (surface tension of water $=7.2\times {10}^{-2}N/m$)

• A. 0.23 m/s
• B. 0.46 m/s
• C. 0.69 m/s
• D. 0.92 m/s

Answer 1

The correct option is A 0.23 m/s

Minimum velocity is given by $v_{min}=\sqrt{2{\left(\frac{Tg}{\rho }\right)}^{1/2}}=1.414{\left(\frac{Tg}{\rho }\right)}^{1/4}$

Given : $T=7.2\times {10}^{-2}N/m$, $\rho ={10}^{3}kg/m^3$
$v_{min}=1.414{\left(\frac{7.2\times {10}^{-2}\times 9.8}{{10}^3}\right)}^{1/4}$
$⟹v_{min}=0.23m/s$