A balloon with mass $m$ is descending down with an acceleration $$a$$ (where, $$a < g$$ ). How much mass should be removed from it so that it starts moving up with an acceleration $$a$$ ?

The speeds of air-flow on the upper and lower surfaces of a wing of an aeroplane are $$v_1$$ and $$v_2$$, respectively. If $$A$$ is the cross-sectional area of the wing and $$\rho$$ is the density of air, then the upward lift is

Water from a tap of cross-sectional area $$1 \mathrm{~cm}^2$$, falls vertically downwards at $$2 \mathrm{~m} / \mathrm{s}$$. The cross sectional area of the stream, $$20 \mathrm{~cm}$$ below the tap is (assume that pressure is constant throughout and the flow is streamlined; $$\left(\mathrm{g}=10 \mathrm{~ms}^{-2}\right)$$

A raft of density 600 g/m$$^3$$ and mass 120 kg floats in water. How much weight can be put on the raft to make it just sink?