A metal sphere of mass '$$m$$' and density '$$\sigma_1$$' falls with terminal velocity through a container containing liquid. The density of liquid is '$$\sigma_2$$'. The viscous force acting on the sphere is

Water flows through a horizontal pipe at a speed '$$\mathrm{V}$$'. Internal diameter of the pipe is '$$\mathrm{d}$$'. If the water is coming out at a speed '$$V_1$$' then the diameter of the nozzle is

Three liquids have same surface tension and densities $$\rho_1, \rho_2$$, and $$\rho_3\left(\rho_1>\rho_2>\rho_3\right)$$. In three identical capillaries rise of liquid is same. The corresponding angles of contact $$\theta_1, \theta_2$$ and $$\theta_3$$ are related as

The height of liquid column raised in a capillary tube of certain radius when dipped in liquid '$$A$$' vertically is $$5 \mathrm{~cm}$$. If the tube is dipped in a similar manner in another liquid '$$B$$' of surface tension and density double the values of liquid '$$A$$', the height of liquid column raised in liquid '$$B$$' would be (Assume angle of contact same)