A barometer tube reads 75 cm of Hg. If tube is gradually inclined at an angle of $30°$ with horizontal, keeping the open end in the mercury container, then find the length of mercury column in the barometer tube

1. 86.7 cm

2. 150 cm

3. 75 cm

4. 92.5 cm

A wooden cube just floats inside water with a 200 gm mass placed on it. When the mass is removed, the cube floats with its top surface 2 cm above the water level. What is the side of the cube?

1. 6 cm

2. 8 cm

3. 10 cm

4. 12 cm

A block of steel of size $5\times 5\times 5 {\mathrm{cm}}^3$ is weighed in water. If relative density of steel is 7, its apparent weight is

1. $6\times 5\times 5\times 5 \mathrm{g} \mathrm{wt}$

2. $4\times 4\times 4\times 7 \mathrm{g} \mathrm{wt}$

3. $5\times 5\times 5\times 7 \mathrm{g} \mathrm{wt}$

4. $4\times 4\times 4\times 6 \mathrm{g} \mathrm{wt}$

A block of wood floats in water with $\frac{4}{5}$th of its volume submerged, but it just floats in another liquid. The density of liquid is (in kg/m³)

1. 750

2. 800

3. 1000

4. 1250

A cubical block is floating in a liquid with one fourth of its volume immersed in the liquid. If whole of the system accelerates upward with acceleration g/4, the fraction of volume immersed in the liquid will be

1. 1/4

2. 1/2

3. 3/4

4. 2/3

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