A small hollow vessel which has a small circular hole of radius r in its base, is immersed in a tank of oil of density and surface tension T. The oil will penetrate into the vessel at a depth of

Step-by-step solution

Let the depth at which the oil penetrates the vessel be h . The hydrostatic pressure exerted by the oil at depth h is given by P = h g . For the oil to enter the vessel through the small hole of radius r , this hydrostatic pressure must overcome the excess pressure due to surface tension at the meniscus formed at the hole. The maximum excess pressure for a meniscus of radius r is P = 2T r . Equating the hydrostatic pressure to the excess pressure: h g = 2T r h = 2T r g Answer: 2T r g