A drop of liquid of density ' ' is floating half immersed in a liquid of density ' d '. If ' T ' is the surface tension, then the diameter of the drop of the liquids is

Step-by-step solution

The drop is in equilibrium under the action of the following forces: Weight of the liquid, W = Mg = 4 3 r ^3 g (downwards) Upthrust = weight of the liquid displaced F _ t = 2 3 r ^3 dg (upwards) Force due to surface tension, F =2 rT (upwards) aligned & Mg = F + F _ t & F = Mg - F _ t & 2 r T= 4 3 r ^3 g- 2 3 r ^3 dg & T = 2 3 r ^2 g- 1 3 r ^2 dg & = r ^2 g ( 2 3 - 1 3 d ) & = r ^2 g ( 2 -d 3 ) & r = 3 ~T ~g (2 - d ) & D = 12 ~T ~g (2 -d) aligned