Fluids Test

Result

Fluids Test - 13

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Weekly Quiz Competition

Question 1
1 / -0

The volume of an air bubble becomes three times as it rises from the bottom of a lake to its surface. Assuming atmospheric pressure to be 75 cm of Hg and the density of water to be 1/10 of the density of mercure, the depth of the lake is

A
5 m

B
10 m

C
15 m

D
20 m

Solution
Question 2
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A hemispherical bowl just floats without sinking in a liquid of density 1.2×10³ kg/m³. If outer diameter and the density of the bowl are 1 m and 2×10⁴ kg/m³ respecitvely, then the inner diameter of the bowl will be

A
1.94 m

B
1.97 m

C
0.98 m

D
1.99 m

Solution

Weight of bowl = mg

where D = Outer diameter,

d = Inner diameter

ρ = Density of bowl

Weight of the liquid displaced by the bowl

where σ is the density of the liquid.

For the flotation

By solving we get d=0.98 m.
Question 3
1 / -0

Spherical balls of radius R are falling in a viscous fluid of velocity v. The retarding viscous force acting on the spherical ball is

A
directly proportional to R but inversely proportional to v.

B
directly proportional to both radius R and velocity v.

C
inversely proportional to both radius R and velocity v

D
inversely proportional to R but directly proportional to velocity v

Solution

Retarding force acting on a ball falling into a viscous fluid F = 6πηRv

Where R=Radius of ball

v=velocity of ball

η=coefficient of viscosity

∴ F∝R and F∝v or in words,

Retarding force is directly proportional to both R and v
Question 4
1 / -0

A ball of radius r and density ρ falls freely under gravity through a distance h before entering water. Velocity of ball does not change even on entering water. If viscosity of water is η, the value of h is given by

A

B

C

D

Solution

Velocity of ball when it strikes the water surface
Question 5
1 / -0

A sniper fires a rifle bullet into a gasoline tank making a hole 53.0 m below the surface of gasoline. The tank was sealed at 3.10 atm. The stored gasoline has a density of 660 kgm^-3. The velocity with which gasoline begins to shoot out of the hole is

A
27.8 ms^-1

B
41.0 ms^-1

C
9.6 ms^-1

D
19.7 ms^-1

Solution
Question 6
1 / -0

A body floats in a liquid contained in a beaker. The whole system as shown falls freely under gravity. The upthrust on the body due to the liquid is

A
zero

B
Equal to the weight of the liquid displaced

C
Equal to the weight of the body in air

D
Equal to the weight of the immersed portion of the body

Solution

where, a = downward acceleration,

V = volume of liquid displaced

But for free fall a =g

∴ Upthrust = 0
Question 7
1 / -0

Water is filled in a cylindrical container to a height of 3 m. The ratio of the cross-sectional area of the orifice and the beaker is 0.1. The square of the speed of the liquid coming out from the orifice is (g = 10 m/s²)

A
50 m²/s²

B
50.5 m²/s²

C
51 m²/s²

D
52 m²/s²

Solution

Let A = cross-section of tank

a = cross-section hole

V = velocity with which level decreases

v = velocity of efflux

From equation of continuity

By using Bemoulli's thearem for energy per unit volume

Energy per unit volume at point A = Energy per unit volume at point B
Question 8
1 / -0

The breaking stress of steel is 7.9×10⁸ N/m² and density is 7.9×10³ kg/m³. What should be the maximum length of a steel wire so that it may not break under its own weight :-

A
5 km

B
10 km

C
15 km

D
20 km

Solution
Question 9
1 / -0

The speeds of air-flow on the upper and lower surfaces of a wing of an aeroplane are v₁ and v₂ respectively. If A is the cross-sectional area of the wing and 'ρ' is the density of air, then the upward lift is :-

A

B

C

D

Solution
Question 10
1 / -0

If h is the height of capillary rise and r be the radius of capillary tube, then which of the following relation will be correct ?

A
hr = constant

B
h/r²= constant

C
hr²= constant

D
h/r = constant

Solution

The height h to which the liquid rises in a capillary tube is given by :

Since, T cos θ, ρ and g are constants. Hence, hr = constant.