Mechanical Properties of Fluids

The surface tension of a soap solution is 3.5 10-2 N/m. The work required to increase the radius of a soap bubble from 1 cm to 2 cm is 10-6 J. The value of is . ( =22/7)

A tub is filled with water and a wooden cube 10 cm 10 cm 10 cm is placed in the water. The wooden cube is found to float on the water with a part of it submerged in water. When a metal coin is placed on the wooden cube, the submerged part is increased by 3.87 cm. The mass of the metal coin is gram. (Take water density as 1 g/cm3 and density of wood as 0.4 g/cm3)

Sixty four raindrops of radius 1 mm each falling down with a terminal velocity of 10 cm/s coalesce to form a bigger drop. The terminal velocity of bigger drop is cm/s.

A soap bubble of surface tension 0.04 N/m is blown to a diameter of 7 cm. If (15000 - x) of work is done in blowing it further to make its diameter 14 cm, then the value of x is . ( = 22/7)

The terminal velocity of a metallic ball of radius 6 mm in a viscous fluid is 20 cm/s. The terminal velocity of another ball of same material and having radius 3 mm in the same fluid will be cm/s.

A cube having a side of 10 cm with unknown mass and 200 gm mass were hung at two ends of a uniform rigid rod of 27 cm long. The rod along with masses was placed on a wedge keeping the distance between wedge point and 200 gm weight as 25 cm. Initially the masses were not at balance. A beaker is placed beneath the unknown mass and water is added slowly to it. At given point the masses were in balance and half volume of the unknown mass was inside the water. (Take the density of unknown mass is more than that of the water, the mass did not absorb water and water density is 1 gm/cm3.) The unknown mass is kg.

The excess pressure inside a soap bubble A in air is half the excess pressure inside another soap bubble B in air. If the volume of the bubble A is n times the volume of the bubble B, then, the value of n is .

A vessel with square cross-section and height of 6 m is vertically partitioned. A small window of 100 cm2 with hinged door is fitted at a depth of 3 m in the partition wall. One part of the vessel is filled completely with water and the other side is filled with the liquid having density 1.5 103 kg/m3. What force one needs to apply on the hinged door so that it does not get opened? (Acceleration due to gravity = 10 m/s2)

In a hydraulic lift, the surface area of the input piston is 6 cm2 and that of the output piston is 1500 cm2. If 100 N force is applied to the input piston to raise the output piston by 20 cm, then the work done is kJ.

An air bubble of radius 1.0 mm is observed at a depth 20 cm below the free surface of a liquid having surface tension 0.095 J/m2 and density 103 kg/m3. The difference between pressure inside the bubble and atmospheric pressure is N/m2. (Take g=10 m/s2)

Two soap bubbles of radius 2 cm and 4 cm , respectively, are in contact with each other. The radius of curvature of the common surface, in cm , is .

A liquid column of height 0.04 cm balances excess pressure of a soap bubble of certain radius. If density of liquid is 8 103 kg m-3 and surface tension of soap solution is 0.28 N m-1, then diameter of the soap bubble is cm. (if g = 10 m s-2)

Small water droplets of radius 0.01 mm are formed in the upper atmosphere and falling with a terminal velocity of 10 cm/s. Due to condensation, if 8 such droplets are coalesced and formed a larger drop, the new terminal velocity will be cm/s.

A big drop is formed by coalescing 1000 small droplets of water. The ratio of surface energy of 1000 droplets to that of energy of big drop is 10x. The value of x is .

[figure] A hydraulic press containing water has two arms with diameters as mentioned in the figure. A force of 10 N is applied on the surface of water in the thinner arm. The force required to be applied on the surface of water in the thicker arm to maintain equilibrium of water is N.

A soap bubble is blown to a diameter of 7 cm. 36960 erg of work is done in blowing it further. If surface tension of soap solution is 40 dyne/cm then the new radius is cm. Take ( = 227 ).

Mercury is filled in a tube of radius 2 cm up to a height of 30 cm. The force exerted by mercury on the bottom of the tube is N. (Given, atmospheric pressure = 105 N m-2, density of mercury = 1.36 104 kg m-3, g = 10 m s-2, = 227)

A plane is in level flight at constant speed and each of its two wings has an area of 40 m2. If the speed of the air is 180 km/h over the lower wing surface and 252 km/h over the upper wing surface, the mass of the plane is kg. (Take air density to be 1 kg m-3 and g = 10 m s-2)

A big drop is formed by coalescing 1000 small identical drops of water. If E1 be the total surface energy of 1000 small drops of water and E2 be the surface energy of single big drop of water, then E1:E2 is x:1 where x= .

In a test experiment on a model aeroplane in wind tunnel, the flow speeds on the upper and lower surfaces of the wings are 70 ms-1 and 65 ms-1 respectively. If the wing area is 2 m2, the lift of the wing is N. (Given density of air =1.2 kg m-3)

The reading of pressure metre attached with a closed pipe is 4.5 104 N/m2. On opening the valve, water starts flowing and the reading of pressure metre falls to 2.0 104 N/m2. The velocity of water is found to be V m/s. The value of V is .