A body of density $\mathrm{\rho }$ is dropped from rest from a height h into a lake of density $\mathrm{\sigma }$, where $\mathrm{\sigma }>\mathrm{\rho }$. Neglecting all dissipative forces, the maximum depth to which the body sinks before returning to float on surface

1. $\frac{\mathrm{h}}{\mathrm{\sigma }-\mathrm{\rho }}$

2. $\frac{\mathrm{h\rho }}{\mathrm{\sigma }}$

3. $\frac{\mathrm{h\rho }}{\mathrm{\sigma }-\mathrm{\rho }}$

4. $\frac{\mathrm{h\sigma }}{\mathrm{\sigma }-\mathrm{\rho }}$

A boat carrying a number of stones is floating in a water tank. If the stones are unloaded into water, the water level in the tank will

1. Remain unchanged

2. Rise

3. Fall

4. Rise or fall depends on the number of stones unloaded

A block of ice is floating on a liquid of specific gravity 1.2 contained in a beaker. When the ice melts completely, the level of liquid in the vessel

1. Increases

2. Decreases

3. Remain unchanged

4. First increases then decreases

Two liquids having densities d₁ and d₂ are mixed in such a way that both have same mass. The density of the mixture is

1. $\frac{{\mathrm{d}}_1+{\mathrm{d}}_2}{2}$

2. $\frac{{\mathrm{d}}_1+{\mathrm{d}}_2}{{\mathrm{d}}_1{\mathrm{d}}_2}$

3. $\frac{{\mathrm{d}}_1{\mathrm{d}}_2}{{\mathrm{d}}_1+{\mathrm{d}}_2}$

4. $\frac{2{\mathrm{d}}_1{\mathrm{d}}_2}{{\mathrm{d}}_1+{\mathrm{d}}_2}$

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