Question

One spherical ball of radius $R$, density d released in a liquid of density $d/2$ attains a terminal velocity $V$. Another ball of radius $2R$ and density $1.5d$, released in the liquid will attain a terminal velocity

• A. $2V$
• B. $4V$
• C. $6V$
• D. $8V$

Answer 1

The correct option is D $8V$

Given, $V=\frac{2R^2(d-d/2)g}{9\eta }$

$V=\frac{2R^2\left(0.5d\right)g}{9\eta }$----------(1)

For case (2),

Terminal Velocity $=\frac{2\left(2R{)}^2\right(1.5d-0.5d)g}{9\eta }$

$TV=\frac{2R^{2}0.5dg(2\times 4)}{9\eta }$ [From (1)]

$T.V=8V$