A liquid flows in the tube from left to right as shown in figure. A₁ and A₂ are the cross-sections of the portions of the tube as shown. The ratio of speed $\frac{{\mathrm{v}}_1}{{\mathrm{v}}_2}$ will be

1. $\frac{{\mathrm{A}}_1}{{\mathrm{A}}_2}$

2. $\frac{{\mathrm{A}}_2}{{\mathrm{A}}_1}$

3. $\sqrt{\frac{{\mathrm{A}}_2}{{\mathrm{A}}_1}}$

4. $\sqrt{\frac{{\mathrm{A}}_1}{{\mathrm{A}}_2}}$

Water $(\mathrm{\rho }=1000 \mathrm{kg}/{\mathrm{m}}^3)$ and kerosene $(\mathrm{\sigma }=800 \mathrm{kg}/{\mathrm{m}}^3)$ are filled in two identical cylindrical vessels. Both vessels have small holes at their bottom. The speed of the water and kerosene coming out of their holes are v₁ and v₂ respectively. Select the correct alternative 

1. ${\mathrm{v}}_1={\mathrm{v}}_2$

2. ${\mathrm{v}}_1=0.8 {\mathrm{v}}_2$

3. $0.8 {\mathrm{v}}_1={\mathrm{v}}_2$

4. ${\mathrm{v}}_1=\sqrt{0.8}{\mathrm{v}}_2$

Water is flowing through a channel (lying in vertical plane) as shown in the figure. Three sections A, B and C are shown. Sections B and C have equal area of cross section. If P_A, P_B and P_C are the pressures at A, B and C respectively then

1. ${\mathrm{P}}_{\mathrm{A}}>{\mathrm{P}}_{\mathrm{B}}={\mathrm{P}}_{\mathrm{C}}$

2. ${\mathrm{P}}_{\mathrm{A}}<{\mathrm{P}}_{\mathrm{B}}<{\mathrm{P}}_{\mathrm{C}}$

3. ${\mathrm{P}}_{\mathrm{A}}<{\mathrm{P}}_{\mathrm{B}}={\mathrm{P}}_{\mathrm{C}}$

4. ${\mathrm{P}}_{\mathrm{A}}>{\mathrm{P}}_{\mathrm{B}}>{\mathrm{P}}_{\mathrm{C}}$

A flat plate of area 0.1 m² is placed on a flat surface and is separated from it by a film of oil 10^-5 m thick whose coefficient of viscocity is 1.5 N sm^-2. The force required to cause the plate to slide on the surface at constant speed of 1 mm s^-1 is

1. 10 N

2. 15 N

3. 20 N

4. 25 N

A ball of density $\mathrm{\sigma }$ and radius r is dropped on the surface of a liquid of density $\mathrm{\rho }$ from certain height. If speed of ball does not change even on entering in liquid and viscosity of liquid is $\mathrm{\eta }$, then the height from which ball dropped is

1. $2\mathrm{g}{\left[\frac{\left(\mathrm{\sigma }-\mathrm{\rho }\right)\mathrm{r}}{\mathrm{\eta }}\right]}^2$

2. $\frac{2\mathrm{g}{(\mathrm{\sigma }-\mathrm{\rho })}^2{\mathrm{r}}^2}{9\mathrm{\eta }}$

3. $\frac{2(\mathrm{\sigma }-\mathrm{\rho }){\mathrm{gr}}^2}{9\mathrm{\eta }}$

4. $2\mathrm{g}{\left[\frac{(\mathrm{\sigma }-\mathrm{\rho }){\mathrm{r}}^2}{9\mathrm{\eta }}\right]}^2$

Viscous drag force depends on

1. Size of body

2. Velocity with which it moves

3. Viscosity of fluid

4. All of these

The terminal velocity of a small sized spherical body of radius r falling vertically in a viscous liquid is related to radius r as-

1. $\mathrm{v}\propto \frac{1}{{\mathrm{r}}^2}$

2. $\mathrm{v}\propto {\mathrm{r}}^2$

3. $\mathrm{v}\propto \frac{1}{\mathrm{r}}$

4. $\mathrm{v}\propto \mathrm{r}$

A spherical ball is dropped in a long column of viscous liquid. The speed v of the ball varies as function of time as

1. 

2. 

3. 

4. 

On putting a capillary tube in a pot filled with water, the level of water rises upto a height of 4 cm in the tube. If a tube of half the diameter is used instead, the water will rise to a height nerly

1. 2 cm

2. 4 cm

3. 8 cm

4. 11 cm

Soap helps in cleaning clothes, because

1. It attracts the dirt particles

2. It decreases the surface tension of water

3. It increases the cohesive force between water molecules

4. It increases the angle of contact