Question

An iron sphere of mass $20\times {10}^{-3}kg$ falls through a viscous liquid with terminal velocity $0.5m{s}^{-1}$.The terminal velocity (in $m{s}^{-1}$) of another iron sphere of mass $54\times {10}^{-2}kg$ is:

• A. $4.5$
• B. $3.5$
• C. $2.5$
• D. $1.5$

Answer 1

Answer: (A)

$4.5$

Let the density and radius of iron be $d$ and $r$ respectively.

So, $\frac{4}{3}\pi r^3\times d=20\times {10}^{-3}$ -----------(1)

and $0.5m/s=\frac{2g{r}^2(T-\sigma )}{9\eta }$ ---------------(2)

Now, in $2^{nd}$ case,

$\frac{4}{3}\pi r_1^3\times d=540\times {10}^{-3}$

$\Rightarrow \frac{r_1^3}{r^3}=27\Rightarrow r_1=3r$[Dividing from(1)]

So, Terminal Velocity $=\frac{2g\left(3r{)}^2\right(T-\sigma )}{9\eta }$

Terminal Velocity $=\frac{2g{r}^2(T-\sigma )}{9\eta }\times 9$ [from(2)]

$\Rightarrow T.V=9\times 0.5m/s$

$=4.5m/s$