Question

A metallic sphere of mass $ M $ falls through glycerine with a terminal velocity $ v $ . If we drop a ball of mass $ 8M $ of same metal into a column of glycerine, the terminal velocity of the ball will be

• A. $ 2v $
• B. $ 4v $
• C. $ 8v $
• D. $ 16v $

Answer 1

Answer: (B)

$ M=\frac{4}{3} \pi r^{3} \rho $ and $ 8M =\frac{4}{3} \pi R^{3}\, \rho $ ,
$ \therefore R^{3}=8r^{3} $ or $ R=2r $
As $ v \propto r^{2} $
$ \therefore \frac{v'}{v}=\left(\frac{R}{r}\right)^{2}=\left(\frac{2r}{r}\right)^{2} $
$ =4 $ or $ v' =4v $