Mechanical Properties of Fluids

A spherical ball of radius 1 10-4 m and density 105 kg/m3 falls freely under gravity through a distance h before entering a tank of water. If after entering in water the velocity of the ball does not change, then the value of h is approximately: (The coefficient of viscosity of water is 9.8 10-6 N s/m2)

1. 2518 m
2. 2396 m
3. 2249 m
4. 2296 m

Correct Bernoulli's equation is (symbols have their usual meaning) :

1. P + 12 gh + 12 v2 = constant
2. P + mgh + 12mv2 = constant
3. P + gh + v2 = constant
4. P + gh + 12 v2 = constant

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)

A cube of ice floats partly in water and partly in kerosene oil. The ratio of volume of ice immersed in water to that in kerosene oil (specific gravity of Kerosene oil = 0.8, specific gravity of ice = 0.9): [figure]

1. 5 : 4
2. 9 : 10
3. 8 : 9
4. 1 : 1

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 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.