A metallic sphere weighing 3 kg in air is held by a string so as to be completely immersed in a liquid of relative density 0.8. The relative density of metallic is 10. The tension in the string is

1. 18.7 N

2. 42.5 N

3. 32.7 N

4. 27.6 N

A rectangular block is $10 \mathrm{cm}\times 10 \mathrm{cm}\times 15 \mathrm{cm}$ in size is floating in water with 10 cm side vertical. If it floats with 15 cm side vertical, then the lever of water will

1. Rise

2. Fall 

3. Remain same

4. Change according to density of block

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