Two cubical blocks identical in dimensions float in water in such a way that 1st block floats with half part immersed in water and second block floats with 3/4 of its volume inside the water. The ratio of densities of blocks is

1. 2 : 3

2. 3 : 4

3. 1 : 3

4. 1 : 4

Which of the following is not the property of an ideal fluid?

1. Fluid flow is irrotational

2. Fluid flow is streamline

3. Fluid is incompressible

4. Fluid is viscous

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.