When an air bubble of radius r rises from the bottom to the surface of a lake its radius becomes $${{5r} \over 4}.$$ Taking the atmospheric pressure to be equal to 10 m height of water column, the depth of the lake would approximately be (ignore the surface tension and the effect of temperature) :

As shown in the figure, forces of 10⁵ N each are applied in opposite directions, on the upper and lower faces of a cube of side 10 cm, shifting the upper face parallel to itself by 0.5 cm. If the side of another cube of the same material is 20 cm, then under similar conditions as above, the displacement will be :

A thin uniform tube is bent into a circle of radius $$r$$ in the vertical plane. Equal volumes of two immiscible liquids, whose densities are $${\rho _1}$$ and $${\rho _2}$$ $$\left( {{\rho _1} > {\rho _2}} \right),$$ fill half the circle. The angle $$\theta $$ between the radius vector passing through the common interface and the vertical is :

Two tubes of radii r₁ and r₂, and lengths l₁ and l₂ , respectively, are connected in series and a liquid flows through each of them in stream line conditions. P₁ and P₂ are pressure differences across the two tubes.

If P₂ is 4P₁ and l₂ is $${{{1_1}} \over 4}$$, then the radius r₂ will be equal to :