Mechanical Properties of Fluids · Question 3

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.

The terminal velocity of a copper ball of radius 5 mm falling through a tank of oil at room temperature is 10 cm s-1. If the viscosity of oil at room temperature is 0.9 kg m-1 s-1, the viscous drag force is :

1. 4.23 10-6 N
2. 8.48 10-3 N
3. 8.48 10-5 N
4. 4.23 10-3 N