What is the excess pressure inside a bubble of soap solution of radius 5.00 mm, given that the surface tension of soap solution at the temperature ($20° \mathrm{C}$) is 2.50 × 10^–2 N/m?

A tank with a square base of an area of 1.0 m² is divided by a vertical partition in the middle. The bottom of the partition has a small-hinged door of area 20 cm². The tank is filled with water in one compartment, and an acid (of relative density 1.7) in the other, both to a height of 4.0 m. What is the force necessary to keep the door close?

During a blood transfusion, the needle is inserted in a vein where the gauge pressure is 2000 Pa. At what height must the blood container be placed so that blood may just enter the vein? [The density of whole blood is 1.06$\times {10}^3 kg m^{-3}$].

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

A plane is in level flight at a constant speed and each of its two wings has an area of 25 m². If the speed of the air is 180 km/h over the lower wing and 234 km/h over the upper wing surface, determine the plane’s mass. (Take air density to be 1 kg m^–3).

In Millikan’s oil drop experiment, what is the terminal speed of an uncharged drop of radius 2.0 × 10^–5 m and density 1.2 × 10³ kg m^–3? (Take the viscosity of air at the temperature of the experiment to be 1.8 × 10^–5 Pa-sec.)

Mercury has an angle of contact equal to 140° with soda-lime glass. A narrow tube of radius 1.00 mm made of this glass is dipped in a trough containing mercury. By what amount does the mercury dip down in the tube relative to the liquid surface outside? [The surface tension of mercury at the temperature of the experiment is 0.465 N m^–1. The density of mercury = 13.6 × 10³ kg m^–3.]

Two narrow bores of diameters 3.0 mm and 6.0 mm are joined together to form a U-tube open at both ends. If the U-tube contains water, what is the difference in its levels in the two limbs of the tube? The surface tension of water at the temperature of the experiment is 7.3 × 10^–2 N m^–1. Take the angle of contact to be zero and the density of water to be 1.0 × 10³ kg m^–3 (g = 9.8 $m s^{-2}$).

The term 'fluid' is used for 

Select wrong statement about pressure

Gauge pressure

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)

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

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

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

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:

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

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?

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

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)

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

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

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

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

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

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

Which of the following is not the property of an ideal fluid?

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 

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

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