A large block of ice 10 cm thick with a vertical hole drilled through it is floating in a lake. The minimum length of the rope required to scoop out a bucket full of water through the hole is (density of ice $=0.9 \mathrm{~g} / \mathrm{cm}^3$ )

Water is flowing on a horizontal fixed surface such that its flow velocity varies with $$y$$ (vertical direction) as $$v=k\left(\frac{2 y^2}{a^2}-\frac{y^3}{a^3}\right)$$. If coefficient of viscosity for water is $$2 \eta$$. What will the shear stress between layers of water at $$y=a$$ ?

A capillary tube is attached horizontally to a constant heat arrangement. If the radius of the capillary tube is increased by 25%, then the rate of flow of liquid will change nearly by

Two drops of equal radius (R) coalesce to form a bigger drop. What is the ratio of surface energy of bigger drop to smaller one?