A small spherical solid ball is dropped in a viscous liquid. Its journey in the liquid is best described in the figure by :

1.  Curve A

2.  Curve B

3.  Curve C

4.  Curve D

Two drops of the same radius are falling through air with a steady velocity of 5 cm per sec. If the two drops coalesce, the terminal velocity would be 

1. 10 cm per sec                               
2. 2.5 cm per sec
3. $5\times (4{)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}$ cm per sec                       
4. $5\times \sqrt{2}$ cm per sec

Two equal drops of water each of radius r are falling through air with a steady velocity

of 8 cm/s . The two drops combine to form a big drop. The terminal velocity of big

drop will be 

(1) $8{\left(2\right)}^{\frac{2}{3}}<mspace\; width="1em"></mspace>cm/s<mspace\; width="1em"></mspace><mspace\; width="1em"></mspace>$

(2) $<mspace\; width="1em"></mspace>16{\left(2\right)}^{\frac{2}{3}}<mspace\; width="1em"></mspace>m<mspace\; width="1em"></mspace><mspace\; width="1em"></mspace><mspace\; width="1em"></mspace><mspace\; width="1em"></mspace>$

(3) $4{\left(2\right)}^{\frac{2}{3}}<mspace\; width="1em"></mspace>cm/s$

(4) 32 cm/s

A ball of mass m and radius r is released in a viscous liquid. The value of its terminal

velocity varies linearly with 

(1) 1/r only

(2) m/r  

(3) ${(m/r)}^{1/2}$

(4) m only 

A raindrop of radius r has a terminal velocity v m/s in air. The viscosity of air is $\eta$ poise. The viscous force on it is F. If the radius of the drop be 2r and the drop falls with terminal velocity in the same air, the viscous force on it will be:

1. F

2. F/2

3. 4F

4. 8F

A small sphere of radius r falls from rest in a viscous liquid. As a result, heat is produced due to the viscous force. The rate of production of heat when the sphere attains its terminal velocity is proportional to

1. ${\mathrm{r}}^3$

2. ${\mathrm{r}}^2$

3. ${\mathrm{r}}^4$

4. ${\mathrm{r}}^5$

If the terminal speed of a sphere of gold $(\mathrm{density}<mspace\; width="1em"></mspace>=<mspace\; width="1em"></mspace>19.5<mspace\; width="1em"></mspace>\mathrm{kg}/{\mathrm{m}}^3)$ is 0.2 m/s in a viscous liquid $(\mathrm{density}<mspace\; width="1em"></mspace>=<mspace\; width="1em"></mspace>1.5<mspace\; width="1em"></mspace>\mathrm{kg}/{\mathrm{m}}^3),$ find the terminal speed of a sphere of silver $(\mathrm{density}<mspace\; width="1em"></mspace>=<mspace\; width="1em"></mspace>10.5<mspace\; width="1em"></mspace>\mathrm{kg}/{\mathrm{m}}^3)$ of the same size in the same liquid

1.  0.4 m/s 

2.  0.133 m/s

3.  0.1 m/s 

4.  0.2 m/s

$\mathrm{A} \mathrm{spherical} \mathrm{solid} \mathrm{ball} \mathrm{of} \mathrm{volume} \mathrm{V} \mathrm{is} \mathrm{made} \mathrm{of} \mathrm{a} \mathrm{material} \mathrm{of} \mathrm{density} {\mathrm{\rho }}_1. \mathrm{It} \mathrm{is} \mathrm{falling} \mathrm{through} \mathrm{a} \mathrm{liquid} \mathrm{of} \mathrm{density} {\mathrm{\rho }}_1 ({\mathrm{\rho }}_2 < {\mathrm{\rho }}_1). \mathrm{Assume} \mathrm{that} \mathrm{the}$
$\mathrm{liquid} \mathrm{applies} \mathrm{a} \mathrm{viscous} \mathrm{force} \mathrm{on} \mathrm{the} \mathrm{ball} \mathrm{that} \mathrm{is} \mathrm{proportional} \mathrm{to} \mathrm{the} \mathrm{square} \mathrm{of} \mathrm{its} \mathrm{speed} \mathrm{v}, \mathrm{i}.\mathrm{e}., {\mathrm{F}}_{\mathrm{viscous}} = –{\mathrm{kv}}^2 (\mathrm{k} > 0). \mathrm{The} \mathrm{terminal}$
$\mathrm{speed} \mathrm{of} \mathrm{the} \mathrm{ball} \mathrm{is}$

1.  $\sqrt{\frac{\mathrm{Vg}\left({\mathrm{\rho }}_1 - {\mathrm{\rho }}_2\right)}{\mathrm{k}}}$

2.  $\frac{{\mathrm{Vg\rho }}_1}{\mathrm{k}}$

3.  $\sqrt{\frac{{\mathrm{Vg\rho }}_1}{\mathrm{k}}}$

4.  $\frac{\mathrm{Vg}\left({\mathrm{\rho }}_1 - {\mathrm{\rho }}_2\right)}{\mathrm{k}}$

A small tiny water droplet is falling towards earth at a uniform speed of 1 cm/s. When 27 such identical droplets combine together to form a bigger drop, then with what uniform velocity will this bigger drop fall?