Mechanical Properties of Fluids

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 tube of length L is shown in the figure. The radius of cross section at the point (1) is 2 cm and at the point (2) is 1 cm , respectively. If the velocity of water entering at point (1) is 2 m/s, then velocity of water leaving the point (2) will be [figure]

1. 4 m/s
2. 6 m/s
3. 2 m/s
4. 8 m/s

A small rigid spherical ball of mass M is dropped in a long vertical tube containing glycerine. The velocity of the ball becomes constant after some time. If the density of glycerine is half of the density of the ball, then the viscous force acting on the ball will be (consider g as acceleration due to gravity)

1. 2Mg
2. 32Mg
3. Mg2
4. Mg

A sphere of relative density and diameter D has concentric cavity of diameter d. The ratio of Dd, if it just floats on water in a tank is :

1. ( - 2 + 2 )1/3
2. ( + 1 - 1 )1/3
3. ( - 1 )1/3
4. ( - 1 )1/3

The excess pressure inside a soap bubble is thrice the excess pressure inside a second soap bubble. The ratio between the volume of the first and the second bubble is:

1. 1 : 9
2. 1 : 27
3. 1 : 81
4. 1 : 3

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.