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

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

Tardigrade Admin · Accepted Answer

M=(4/3) π r3 ρ and 8M =(4/3) π R3 ρ , ∴ R3=8r3 or R=2r As v propto r2 ∴ (v'/v)=((R/r))2=((2r/r))2 =4 or v' =4v

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

$2 v$

$4 v$

$8 v$

$16 v$

$M = \frac{4}{3} π r^{3} ρ$ and $8 M = \frac{4}{3} π R^{3} ρ$ ,
$∴ R^{3} = 8 r^{3}$ or $R = 2 r$
As $v \propto r^{2}$
$∴ \frac{v ^{'}}{v} = (\frac{R}{r})^{2} = (\frac{2 r}{r})^{2}$
$= 4$ or $v^{'} = 4 v$

Q. 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

2v

4v

8v

16v