Fluids Test

Result

Fluids Test - 5

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Weekly Quiz Competition

Question 1
1 / -0

A metal sphere connected by a string is dipped in a liquid of density ρ_ρ as shown in figure. The pressure at the bottom of the vessel will be, (p₀ atmospheric pressure)

A
p= p₀+ ρgh

B
p > p₀+ ρgh

C
p < p₀+ρgh

D
p₀

Solution

Upthrust on sphere from the liquid makes equal and opposite pair of forces. Hence there will be no effect on the pressure at bottom of vessel. Or p = p₀+ ρgh
Question 2
1 / -0

Two soap bubbles of radii r₁ and r₂ equal to 4 am and 5 sm are touching each other over a common surface S₁S₂ (shown in figure). Its radius will be

A
4 cm

B
20 cm

C
5 cm

D
4.5 cm

Solution
Question 3
1 / -0

A piece of ice is floating in a beaker containing water when ice melts the temperature falls from 20°C to 4°C, level of water

A
remains uncharged

B
falls

C
rises

D
changes erratically

Solution

As the density of water at 4°C is maximum, the volume of liquid decreases which makes the level fall.
Question 4
1 / -0

The work done in blowing a bubble of radius is W, then the work done in making a bubble of radius 2R from that solution is

A
W/2

B
2W

C
4W

D

Solution
Question 5
1 / -0

When the system shown in the adjoining figure is in equilibrium and if the areas of cross section of the smaller piston and bigger piston are a and 10 a mass on smaller and bigger pistons are m amd M, then

A
m=M

B
m= 10M

C
M= 10 m

D
M= 100 m

Solution
Question 6
1 / -0

A wooden block, with a coin placed on its top, floats in water as shown in fig. the distance l and h are shown there. After some time the coin falls into the water. Then

A
l decreases and h increases

B
l increases and h decreases

C
Both l and h increase

D
Both l and h decrease

Solution

As the block moves up with the fall of coin, l decreases, similarly h will also decrease because when the coin is in water, it displacees water equal to its own volume only.
Question 7
1 / -0

What is the velocity v of a metallic ball of radius r failing in a tank of liquid at the instant when its acceleration is one-half that of a freely falling body? (The densities of metal and of liquid are ρ and σ respectively, and the viscosity of the liquid is h)

A

B

C

D

Solution

We know that terminal velocity is given by
Question 8
1 / -0

A tank is filled with water upto a height H. Water is allowed to come out of a hole P in one pf the walls at a depth D below the surface of water. Express the horizontal distance x in terms of H and D

A

B

C

D

Solution

Time taken by water to reach the bottom
Question 9
1 / -0

A U-tube od uniform cross section as shown in figure is partially filled with a liquid I. Another liquid II which does not mix with liquid I is poured into one side. It is found that the liquid levels of the two sides of the tube are the same, while the level of liquid I has risen by 2cm. If the specific gravity of liquid I is 1.1 the specific gravity of liquid II must be

A
1.12

B
1.1

C
1.05

D
1.0

Solution

Equating pressure at BD (line of constant pressure)

∴ 2 × ρ'g = 2 × 1.1 × g

ρ' = 1.1
Question 10
1 / -0

A tube of length h (which is wide enough so that surface tension effects can be neglected) is filled with air and closed at one end is lowered into a tank of mercury to a depth h as shown; so that mercury rises a distance x into the tube. If the mercury barometer also reads 'h', then

A
h (h−x) = h²

B
(2h−x) (h−x) = h²

C
(2h−x) (h+x) = h²

D
(2h) (h−x) = h²

Solution

P V= constant

If a is area cross section of the tube (ah)

h= a (h-x) (h+h-x)

hence