Mechanical Properties of Fluids

A small ball of mass m and density is dropped in a viscous liquid of density 0. After sometime, the ball falls with constant velocity. The viscous force on the ball is :

1. mg (1 - 0 )
2. mg ( 0 - 1 )
3. mg (1 - 0 )
4. mg (1 + 0 )

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 .

Pressure inside a soap bubble is greater than the pressure outside by an amount : (given : R = Radius of bubble, S = Surface tension of bubble)

1. SR
2. 4SR
3. 4RS
4. 2SR

Given below are two statements : In the light of the above statement, choose the correct answer from the options given below.

1. Statement I is true and Statement II is false
2. Statement I is false but Statement II is true
3. Both Statement I and Statement II are true
4. Both Statement I and Statement II are false

[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.

Given below are two statements : In the light of the above statements, choose the most appropriate answer from the options given below.

1. Statement I is correct but Statement II is incorrect.
2. Both Statement I and Statement II are correct.
3. Both Statement I and Statement II are incorrect.
4. Statement I is incorrect but Statement II is correct.

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 ).

Given below are two statements : In the light of the above statements, choose the correct answer from the options given below :

1. Both Statement I and Statement II are false.
2. Both Statement I and Statement II are true.
3. Statement I is false but Statement II is true.
4. Statement I is true but Statement II is false.

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)