The pressure of confined air is p. If the atmospheric pressure is P, then

1. P is equal to p

2. P is less than p

3. P is greater than p

4. P may be less or greater than p depending on the mass of the confined air

Figure shows a container filled with a liquid of density $\mathrm{\rho }$. Four points A, B, C and D lie on the diametrically opposite points of a circle as shown. Points A and C lie on vertical line and points B and D lie on horizontal line. The incorrect statement is (p_A, p_B, p_C, p_D are absolute pressure at the respective points)

1. ${\mathrm{p}}_{\mathrm{D}}={\mathrm{p}}_{\mathrm{B}}$

2. ${\mathrm{p}}_{\mathrm{A}}<{\mathrm{p}}_{\mathrm{B}}={\mathrm{p}}_{\mathrm{D}}<{\mathrm{p}}_{\mathrm{C}}$

3. ${\mathrm{p}}_{\mathrm{D}}={\mathrm{p}}_{\mathrm{B}}=\frac{{\mathrm{p}}_{\mathrm{C}}-{\mathrm{p}}_{\mathrm{A}}}{2}$

4. ${\mathrm{p}}_{\mathrm{D}}={\mathrm{p}}_{\mathrm{B}}=\frac{{\mathrm{p}}_{\mathrm{C}}+{\mathrm{p}}_{\mathrm{A}}}{2}$

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