Question

If 2 equal rain drops falling through air the with equal steady velocity of 5 cm/s coalesce. Find out the new terminal velocity of a big drop.

Answer 1

∵ v_t ∝ r²

^{\(\therefore\ \frac{v_2}{v_1} = \frac{R^2}{r^2} = (\frac{R}{r})^2\ ....(1)\)}

∵ Volume of big drop = 2 x Volume of small drop

or \(\frac{4}{3}\pi R^3 = 2\times \frac{4}{3}\pi r^3\)

or R = 2^1/3 r

∴ From equation (1), \(\frac{v_2}{v_1} = (\frac{2^{1/3}r}{r}) = 2^{2/3}\)

∴ v₂ = v₁(2)^2/3 = 5(2)^2/3 cm/s

Based on Equation of Continuity