Test on Mechanical Properties of Fluids-2

If two soap bubbles of different radii are connected by a tube,

There is a circular rube in a vertical plane. Two liquids which do not mix and of densities d₁ and d₂ are filled in the tube. Each liquid subtends 90 ° angle at centre. Radius joining their interface makes an angle α with vertical, ratio d₁/d₂ is

On heating water, bubbles being formed at the bottom of the vessel detach and rise. Take the bubbles to be spheres of radius R and making a circular contact of radius r with the bottom of the vessel. If r < < R. and the surface tension of water is T, value of r just before bubbles detach is : (density of water is r_w)

A water fountain on the ground sprinkles water all around it. If the speed of water coming out of the fountain is v, the total area around the fountain that gets wet is

A ball is made of a material of density ρ where ρ_oil < ρ < ρ_water with ρ_oil and ρ_water representing the densities of oil and water, respectively. The oil and water are immiscible. If the above ball is in equilibrium in a mixture of this oil and water, which of the following pictures represents its equilibrium position ?