The volume of an air bubble is doubled as it rises from the bottom of lake to its surface. The atmospheric pressure is 75 cm of mercury. The ratio of density of mercury to that of lake water is $\frac{40}{3}$. The depth of the lake in metre is

1. 10

2. 15

3. 20

4. 25

A beaker containing a liquid of density $\mathrm{\rho }$ moves up with an acceleration 'a'. The pressure due to the liquid at a depth h below free surface of the liquid is

1. $\mathrm{h\rho g}$

2. $\mathrm{h\rho }(\mathrm{g}-\mathrm{a})$

3. $\mathrm{h\rho }(\mathrm{g}+\mathrm{a})$

4. $2\mathrm{h\rho g} \left(\frac{\mathrm{g}+\mathrm{a}}{\mathrm{g}-\mathrm{a}}\right)$

A barometer kept in an elevator reads 76 cm when it is at rest. If the elevator goes up with some acceleration, the reading will be

1. 76 cm

2. > 76 cm

3. < 76 cm

4. Zero

In a hydraulic jack as shown, the mass of the car, W=800 kg, ${\mathrm{A}}_1=10 {\mathrm{cm}}^2, {\mathrm{A}}_2=10 {\mathrm{m}}^2$. The minimum force F required to lift the car is:

1. 1 N

2. 0.8 N

3. 8 N

4. 16 N

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