Eight spherical rain drops of the same mass and radius are falling down with a terminal speed of 6 ~cm - s ⁻¹ . If they coalesce to form one big drop, what will be the terminal speed of bigger drop? (Neglect the buoyancy of the air)

Step-by-step solution

Let now radius of big drop is R . Then, aligned 4 3 R^3 & = 4 3 r^3 8 R & =2 r aligned where r is radius of small drops. Now, terminal velocity of drop in liquid. v_e= 2 9 r^2 ( - ) g where is coefficient of viscosity and is density of drop is density of liquid. Terminal speed drop is 6 ~cm ~s ⁻¹ Let terminal velocity becomes v^ after coalesce, then Dividing Eq. (i) by Eq. (ii), we get aligned 6 v^ = 2 9 r^2 ( - ) g 2 9 R^2 ( - ) g or 6 v^ = r^2 (2 r)^2 or v^ =24 ~cm ~s ⁻¹ aligned