Two small spherical metal balls, having equal masses, are made from materials of densities \(\rho_1\) and \(\rho_2\) such that ${}_{}$\(\rho_1=8\rho_2\) and having radii of \(1\) mm and \(2\) mm, respectively. They are made to fall vertically (from rest) in a viscous medium whose coefficient of viscosity equals \(\eta\) and whose density is \(0.1\rho_2\)${\mathrm{}}_{}$. The ratio of their terminal velocities would be:

1.	\(\dfrac{79}{72}\)	2.	\(\dfrac{19}{36}\)
3.	\(\dfrac{39}{72}\)	4.	\(\dfrac{79}{36}\)

In a U-tube, as shown in the figure, the water and oil are in the left side and right side of the tube respectively. The height of the water and oil columns are \(15~\text{cm}\) and \(20~\text{cm}\) respectively. The density of the oil is: 
 \(\left[\text{take}~\rho_{\text{water}}= 1000~\text{kg/m}^{3}\right]\)$$

              
1. \(1200~\text{kg/m}^{3}\)
2. \(750~\text{kg/m}^{3}\)
3. \(1000~\text{kg/m}^{3}\)
4. \(1333~\text{kg/m}^{3}\)

An incompressible liquid travels as shown in the figure. The speed of the fluid in the lower branch will :

1. 1 m/s

2. 1.5 m/s

3. 2.25 m/s

4. 3 m/s

An ice block of volume $\frac{32\mathrm{\pi }}{3}c{m}^3$is placed in
gravity free space. When ice completely melts, then
its surface area - (Neglect difference in density of ice and water)

1. $4\mathrm{\pi } {\mathrm{cm}}^2$

2. $8\mathrm{\pi } {\mathrm{cm}}^2$

3. $16\mathrm{\pi } {\mathrm{cm}}^2$

4. $\mathrm{\pi } {\mathrm{cm}}^2$

Two horizontal pipes have radii in ratio 1 : 2 and
lengths in ratio 1 : 2. Same viscous fluid flows at
same pressure difference in both the pipes. The flow
rates are in the ratio

1. 1 : 2

2. 1 : 4

3. 1 : 8

4. 1 : 16

$1 {\mathrm{m}}^3$ water is brought inside the lake up to 200 metres depth from the surface of the lake. What will be changed in the volume when the bulk modulus of elastically of water is 22000 atmosphere? 
$(\mathrm{density} \mathrm{of} \mathrm{water} \mathrm{is} 1 \times {10}^3 \mathrm{kg}/{\mathrm{m}}^3 \mathrm{atmosphere} \mathrm{pressure} = {10}^{5 }\mathrm{N}/{\mathrm{m}}^2 \mathrm{and} \mathrm{g} = 10 \mathrm{m}/{\mathrm{s}}^2 )$

1.  8.9 × ${10}^{–3} {\mathrm{m}}^3$

2.  7.8 × ${10}^{–3} {\mathrm{m}}^3$

3.  9.1 × ${10}^{–4 }{\mathrm{m}}^3$

4.  8.7 × ${10}^{–4 }{\mathrm{m}}^3$

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

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

If the terminal speed of a sphere of gold $(\mathrm{density} = 19.5 \mathrm{kg}/{\mathrm{m}}^3)$ is 0.2 m/s in a viscous liquid $(\mathrm{density} = 1.5 \mathrm{kg}/{\mathrm{m}}^3),$ find the terminal speed of a sphere of silver $(\mathrm{density} = 10.5 \mathrm{kg}/{\mathrm{m}}^3)$ 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

By sucking through a straw, a student can reduce the pressure in his lungs to 750 mm of Hg $(\mathrm{density} = 13.6 \mathrm{gm}/{\mathrm{cm}}^3).$ Using the straw, he can drink water from a glass up to a maximum depth of :

1.  10 cm 

2.  75 cm

3.  13.6 cm 

4.  1.36 cm

Three liquids of densities \(d,\) \(2d\) and \(3d\) are mixed in equal proportions of weights. The relative density of the mixture is: