Question

Eight drops of a liquid of density $ \rho $ and each of radius a are falling through air with a constant velocity $ 3.75\,cm{{s}^{-1}} $ . When the eight drops coalesce to form a single drop the terminal velocity of the new drop will be

• A. $ 1.5\times {{10}^{-2}}m{{s}^{-1}} $
• B. $ 2.4\times {{10}^{-2}}m{{s}^{-1}} $
• C. $ 0.75\times {{10}^{-2}}m{{s}^{-1}} $
• D. $ 25\times {{10}^{-2}}m{{s}^{-1}} $
• E. $ 15\times {{10}^{-2}}m{{s}^{-1}} $

Answer 1

Answer: (E)

Terminal velocity of a single drop,
$ v=3.75\text{ }cm{{s}^{-1}}=3.75\times {{10}^{-2}}m{{s}^{-1}} $
Terminal velocity of the big drop
$ V={{n}^{2/3}}v={{(8)}^{2/3}}\times 3.75\times {{10}^{-2}} $
$ =4\times 3.75\times {{10}^{-2}} $
$ =15\times {{10}^{-2}}m{{s}^{-1}} $