A long cylindrical glass vessel has a pinhole of diameter (0.2 ~mm ) at its bottom. The depth to which the vessel can be lowered vertically in a deep water bath without the water entering into the vessel is (surface tension of water, (T=0.07 Nm ⁻¹ ), acceleration due to gravity, (g=10 ~ms ⁻² ) )

Step-by-step solution

Given, diameter of a pinhole, (d=0.2 ~mm ) ( ) radius of pinhole, (r= 0.2 2 =0 l mm =0 . I 10⁻³ ~m ) When the hydrostatic pressure is equal to the excess pressure, then water cannot enter the pinhole Hence, (h g= 2 T r ) where, (h= ) depth up to which cylinder is immersed. ( = ) density of water (T= ) surface tension of water and (r= ) radius of a pinhole ( aligned h & = 2 T g r = 2 0.07 10^3 10 0.1 10⁻³ & =0.14 ~m =14 ~cm aligned ) Hence, the depth to which the vessel can be lowered vertically in a deep water bath