Mechanical Properties of Fluids · Question 2

In the measurement of viscosity of liquids using terminal velocity experiment, spherical balls of same radius but having different densities are used. The variation of the terminal velocity (v) with the ratio of density of spherical ball ( ) to density of the liquid ( ), is best represented by:

1. [figure]
2. [figure]
3. [figure]
4. [figure]

A balloon is made of a material of surface tension S and its inflation outlet (from where gas is filled in it) has small area A. It is filled with a gas of density and takes a spherical shape of radius R. When the gas is allowed to flow freely out of it, its radius r changes from R to 0 (zero) in time T. If the speed v(r) of gas coming out of the balloon depends on r as ra and T S A R then

1. a = - 12, = - 12, = -1, = 12, = 72
2. a = 12, = 12, = - 12, = 12, = 72
3. a = 12, = 12, = -1, = +1, = 32
4. a = - 12, = - 12, = -1, = - 12, = 52

Consider a water tank shown in the figure. It has one wall at x = L and can be taken to be very wide in the z direction. When filled with a liquid of surface tension S and density , the liquid surface makes angle 0 ( 0 1) with the x-axis at x = L. If y(x) is the height of the surface then the equation for y(x) is: [figure] (take (x) = (x) = (x) = dydx, g is the acceleration due to gravity)

1. d2ydx2 = gS
2. dydx = gSx
3. d2ydx2 = gSx
4. d2ydx2 = gSy

A thin flat circular disc of radius 4.5 cm is placed gently over the surface of water. If surface tension of water is 0.07 N m-1, then the excess force required to take it away from the surface is

1. 19.8 mN
2. 198 N
3. 1.98 mN
4. 99 N

An ideal fluid is flowing in a non-uniform cross-sectional tube XY (as shown in the figure) from end X to end Y. If K1 and K2 are the kinetic energy per unit volume of the fluid at X and Y respectively, then the correct option is : [figure]

1. K1 = K2
2. 2K1 = K2
3. K1 > K2
4. K1 < K2

The amount of energy required to form a soap bubble of radius 2 cm from a soap solution is nearly: (surface tension of soap solution = 0.03 N m-1)

1. 5.06 10-4 J
2. 3.01 10-4 J
3. 50.1 10-4 J
4. 30.16 10-4 J

The venturi-meter works on :

1. Bernoulli's principle
2. The principle of parallel axes
3. The principle of perpendicular axes
4. Huygens' principle

A spherical ball is dropped in a long column of a highly viscous liquid. The curve in the graph shown, which represents the speed of the ball (v) as a function of time (t) is [figure]

1. A
2. B
3. C
4. D

If a soap bubble expands, the pressure inside the bubble

1. Decreases
2. Increases
3. Remains the same
4. Is equal to the atmospheric pressure

Two copper vessels A and B have the same base area but of different shapes. A takes twice the volume of water as that B requires to fill upto a particular common height. Then the correct statement among the following is :

1. Vessel B weighs twice that of A.
2. Pressure on the base area of vessels A and B is same.
3. Pressure on the base area of vessels A and B is not same.
4. Both vessels A and B weigh the same.