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A ball of mass $10 k g$ and density $1 g m / {c m}^{3}$ is attached to the base of a container having a liquid of density $1.1 g m / {c m}^{3}$ , with the help of a spring as shown in the figure. The container is going up with an acceleration $2 m / s^{2}$ . If the spring constant of the spring is $200 N / m$ , the elongation in the spring is -

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Important Questions on Fluid Mechanics

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Physics>Mechanics>Fluid Mechanics>Archimedes Principle and Buoyancy

Consider a solid sphere of radius

R

and mass density

ρ (r) = ρ_{0} (1 - \frac{r^{2}}{R^{2}}), 0 < r \leq R .

The minimum density of a liquid in which it will float is:

MEDIUM

Physics>Mechanics>Fluid Mechanics>Archimedes Principle and Buoyancy

A submarine experiences a pressure of

5.05 \times 10^{6} P a

at a depth of

d_{1}

in a sea. When it goes further to a depth of

d_{2}

, it experiences a pressure of

8.08 \times 10^{6} P a

. Then

d_{2} - d_{1}

is approximately (density of water

= 10^{3} k g / m^{3}

and acceleration due to gravity

= 10 m s^{- 2}

HARD

Physics>Mechanics>Fluid Mechanics>Archimedes Principle and Buoyancy

A wooden block floating in a bucket of water has

\frac{4}{5}

of its volume submerged. When certain amount of an oil is poured into the bucket, it is found that the block is just under the oil surface with half of its volume under water and half in oil. The density of oil relative to that of water is:

EASY

Physics>Mechanics>Fluid Mechanics>Archimedes Principle and Buoyancy

A block of wood floats in water with

(4 / 5)^{th}

of its volume submerged. If the same block just floats in a liquid, the density of liquid in

(kg m^{- 3})

MEDIUM

Physics>Mechanics>Fluid Mechanics>Archimedes Principle and Buoyancy

A body of density

ρ

and volume

V

is lifted through height

h

in a liquid of density

σ (< ρ) .

The increase in potential energy of the body is

MEDIUM

Physics>Mechanics>Fluid Mechanics>Archimedes Principle and Buoyancy

An ice-berg of density

900 kg m^{- 3}

is floating in water of density

1000 kg m^{- 3}

. The percentage of volume of ice-berg outside the water is

MEDIUM

Physics>Mechanics>Fluid Mechanics>Archimedes Principle and Buoyancy

A cubical block of side

0.5 m

floats on water with

30 %

of its volume under water. What is the maximum weight that can be put on the block without fully submerging it under water?
[Take, density of water

= 10^{3} k g / m^{3}

]

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Physics>Mechanics>Fluid Mechanics>Archimedes Principle and Buoyancy

A vessel contains oil (density

= 0.8 g {cm}^{- 3}

) over mercury (density

= 13.6 g {cm}^{- 3}

). A homogeneous sphere floats with half of its volume immersed in mercury and the other half in oil. The density of the material of the sphere (in

g {cm}^{- 3}

) is

MEDIUM

Physics>Mechanics>Fluid Mechanics>Archimedes Principle and Buoyancy

A box, when hung from a spring balance shows a reading of

50 kg

. If the same box is hung from the same spring balance inside an evacuated chamber, the reading on the scale will be

HARD

Physics>Mechanics>Fluid Mechanics>Archimedes Principle and Buoyancy

A machine is blowing spherical soap bubbles of different radii filled with helium gas. It is found that if the bubbles have a radius smaller than

1 cm

, then they sink to the floor in still air. Larger bubbles float in the air. Assume that the thickness of the soap film in all bubbles is uniform and equal. Assume that the density of soap solution is the same as that of water

(1000 kg m^{- 3}) .

The density of helium inside the bubbles and air are

0.18 kg m^{- 3} & 1.23 kg m^{- 3}

, respectively. Then the thickness of the soap film of the bubbles is

(1 μm = 10^{- 6} m)

EASY

Physics>Mechanics>Fluid Mechanics>Archimedes Principle and Buoyancy

Iceberg floats in water with part of it submerged. What is the fraction of the volume of iceberg submerged if the density of ice is

ρ_{i} = 0.917 g {cm}^{- 3}

MEDIUM

Physics>Mechanics>Fluid Mechanics>Archimedes Principle and Buoyancy

A uniform cylinder of length

L

and mass

M

having cross-sectional area

A

is suspended, with its length vertical, from a fixed point by a massless spring, such that it is half submerged in a liquid of density

σ

at equilibrium position. The extension

x_{0}

of the spring when it is in equilibrium is :

HARD

Physics>Mechanics>Fluid Mechanics>Archimedes Principle and Buoyancy

A body of density

d_{1}

is counter poised by

M g

of weights of density

d_{2}

in air of density

d

. Then the true mass of the body is

EASY

Physics>Mechanics>Fluid Mechanics>Archimedes Principle and Buoyancy

An aluminium sphere is dipped into water. Which of the following is true?

EASY

Physics>Mechanics>Fluid Mechanics>Archimedes Principle and Buoyancy

The percentage volume of ice-cube outside the water when it is floating in water is ___. (Density of ice is

900 kg m^{- 3}

, Density of water

1000 kg m^{- 3}

)

HARD

Physics>Mechanics>Fluid Mechanics>Archimedes Principle and Buoyancy

A block of wood is floating on water at

0 ° C

with volume

V_{0}

above water. When the temperature of water increases from

0

10 ° C,

the change in the volume of the block that is above water is best described schematically by the graph.

HARD

Physics>Mechanics>Fluid Mechanics>Archimedes Principle and Buoyancy

A very large block of ice of the size of a volleyball court and of uniform thickness of

8 m

is floating on water. A person standing near its edge wishes to fetch a bucketful of water using a rope. The smallest length of rope required for this is about

EASY

Physics>Mechanics>Fluid Mechanics>Archimedes Principle and Buoyancy

A body

P

floats in water with half its volume immersed. Another body

Q

floats in a liquid of density

\frac{3}{4} t h

of the density of water with two-third of the volume immersed. The ratio of density of

P

to that of

Q

HARD

Physics>Mechanics>Fluid Mechanics>Archimedes Principle and Buoyancy

A cylindrical block of wood (density = $650 kg m^{- 3}$ ), of base area $30 {cm}^{2}$ and height $54 cm$ , floats in a liquid of density $900 kg m^{- 3}$ . The block is depressed slightly and then released. The time period of the resulting oscillations of the block would be equal to that of a simple pendulum of length (nearly) :

EASY

Physics>Mechanics>Fluid Mechanics>Archimedes Principle and Buoyancy

Two non-mixing liquids of densities

ρ

and

n ρ (n > 1)

are put in a container. The height of each liquid is

h.

A solid cylinder of length

L

and density

d

is put in this container. The cylinder floats with its axis vertical and length

p L (p < 1)

in the denser liquid. The density

d

is equal to:

Important Questions on Fluid Mechanics

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