Two identical drops of water are falling through air with steady velocity ' V '. If the two drops come together to form a single drop. The new velocity of the single drop is

When an air bubble rises from the bottom of lake to the surface, its radius is doubled. The atmospheric pressure is equal to that of a column of water of height ' $H$ '. The depth of the lake is

Water is flowing in a conical tube as shown in figure. Velocity of water at area ' $\mathrm{A}_2$ ' is $60 \mathrm{~cm} / \mathrm{s}$. The value of ' $\mathrm{A}_1$ ' and ' $\mathrm{A}_2$ ' is $10 \mathrm{~cm}^2$ and $5 \mathrm{~cm}^2$ respectively. The pressure difference at both the cross-section is

A hemispherical portion of radius ' $R$ ' is removed from the bottom of a cylinder of radius ' R '. The volume of the remaining cylinder is ' V ' and its mass is ' M '. It is suspended by a string in a liquid of density ' $\rho$ ', where it stays vertical. The upper surface of the cylinder is at a depth ' $h$ ' below the liquid surface. The force on the bottom of the liquid is