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Mechanical Properties of Fluids

143363 A vessel contains oil (density $ρ_{1}$ ) over a liquid of density $ρ_{2}$ . A homogeneous sphere of volume $V$ floats with half of its volume immersed in the liquid and the other half in oil. The weight of the sphere is

1

V (ρ_{2} - ρ_{1}) / 2

2

V (ρ_{2} + ρ_{1}) g / 2

3

V (ρ_{2} + ρ_{1})

4

V (ρ_{2} + ρ_{1}) / 2

Explanation:

B Weight of floating body $=$ Weight of liquid displaced
$W = ρ_{1} \times \frac{V}{2} \times g + ρ_{2} \times \frac{V}{2} \times g$
$= \frac{V (ρ_{1} + ρ_{2}) g}{2}$

NDA (I) 2010

Mechanical Properties of Fluids

143306 A spherical object of density $ρ$ is immersed in a fluid of density $σ$ . The object will move

1 downwards if

ρ > σ

2 downwards if

σ > ρ

3 upwards if

ρ < σ

4 upwards if

ρ > σ

Explanation:

A ,c) : If the density of object is greater than that of liquid $(ρ > σ)$ , then object will move downward,
If the density of object is lesser than that of liquid $(ρ <$ $σ$ ), then object move upward

UPSEE - 2011

Mechanical Properties of Fluids

143318 A ball floats on the surface of water in a container exposed to the atmosphere. When the container is covered and the air is partially removed, then the ball

1 rises

2 gets immersed more in water

3 remains immersed at its former depth

4 may rise or sink.

COMEDK 2020

Mechanical Properties of Fluids

143331 An aluminium sphere is dipped into water. Which of the following is true ?

1 Buoyancy will be less in water at

0^{\circ} C

than
that is water at

4^{\circ} C

2 Buoyancy will be more in water at

0^{\circ} C

than
that in water at

4^{\circ} C

3 Buoyancy in water at

0^{\circ} C

will be same as that in water at

4^{\circ} C

4 Buoyancy may be more or less in water

4^{\circ} C

depending on the radius of the sphere

Explanation:

A Buoyancy depends on the fluid in which the body is immersed. It depends upon the density of the fluid. Since density of water is maximum at $4^{\circ} C$ so the buoyancy at $4^{\circ} C$ will be maximum.

Karnataka CET-2019

Mechanical Properties of Fluids

143363 A vessel contains oil (density $ρ_{1}$ ) over a liquid of density $ρ_{2}$ . A homogeneous sphere of volume $V$ floats with half of its volume immersed in the liquid and the other half in oil. The weight of the sphere is

1

V (ρ_{2} - ρ_{1}) / 2

2

V (ρ_{2} + ρ_{1}) g / 2

3

V (ρ_{2} + ρ_{1})

4

V (ρ_{2} + ρ_{1}) / 2

Explanation:

B Weight of floating body $=$ Weight of liquid displaced
$W = ρ_{1} \times \frac{V}{2} \times g + ρ_{2} \times \frac{V}{2} \times g$
$= \frac{V (ρ_{1} + ρ_{2}) g}{2}$

NDA (I) 2010

Mechanical Properties of Fluids

143306 A spherical object of density $ρ$ is immersed in a fluid of density $σ$ . The object will move

1 downwards if

ρ > σ

2 downwards if

σ > ρ

3 upwards if

ρ < σ

4 upwards if

ρ > σ

Explanation:

A ,c) : If the density of object is greater than that of liquid $(ρ > σ)$ , then object will move downward,
If the density of object is lesser than that of liquid $(ρ <$ $σ$ ), then object move upward

UPSEE - 2011

Mechanical Properties of Fluids

143318 A ball floats on the surface of water in a container exposed to the atmosphere. When the container is covered and the air is partially removed, then the ball

1 rises

2 gets immersed more in water

3 remains immersed at its former depth

4 may rise or sink.

COMEDK 2020

Mechanical Properties of Fluids

143331 An aluminium sphere is dipped into water. Which of the following is true ?

1 Buoyancy will be less in water at

0^{\circ} C

than
that is water at

4^{\circ} C

2 Buoyancy will be more in water at

0^{\circ} C

than
that in water at

4^{\circ} C

3 Buoyancy in water at

0^{\circ} C

will be same as that in water at

4^{\circ} C

4 Buoyancy may be more or less in water

4^{\circ} C

depending on the radius of the sphere

Explanation:

A Buoyancy depends on the fluid in which the body is immersed. It depends upon the density of the fluid. Since density of water is maximum at $4^{\circ} C$ so the buoyancy at $4^{\circ} C$ will be maximum.

Karnataka CET-2019

Mechanical Properties of Fluids

143363 A vessel contains oil (density $ρ_{1}$ ) over a liquid of density $ρ_{2}$ . A homogeneous sphere of volume $V$ floats with half of its volume immersed in the liquid and the other half in oil. The weight of the sphere is

1

V (ρ_{2} - ρ_{1}) / 2

2

V (ρ_{2} + ρ_{1}) g / 2

3

V (ρ_{2} + ρ_{1})

4

V (ρ_{2} + ρ_{1}) / 2

Explanation:

B Weight of floating body $=$ Weight of liquid displaced
$W = ρ_{1} \times \frac{V}{2} \times g + ρ_{2} \times \frac{V}{2} \times g$
$= \frac{V (ρ_{1} + ρ_{2}) g}{2}$

NDA (I) 2010

Mechanical Properties of Fluids

143306 A spherical object of density $ρ$ is immersed in a fluid of density $σ$ . The object will move

1 downwards if

ρ > σ

2 downwards if

σ > ρ

3 upwards if

ρ < σ

4 upwards if

ρ > σ

Explanation:

A ,c) : If the density of object is greater than that of liquid $(ρ > σ)$ , then object will move downward,
If the density of object is lesser than that of liquid $(ρ <$ $σ$ ), then object move upward

UPSEE - 2011

Mechanical Properties of Fluids

143318 A ball floats on the surface of water in a container exposed to the atmosphere. When the container is covered and the air is partially removed, then the ball

1 rises

2 gets immersed more in water

3 remains immersed at its former depth

4 may rise or sink.

COMEDK 2020

Mechanical Properties of Fluids

143331 An aluminium sphere is dipped into water. Which of the following is true ?

1 Buoyancy will be less in water at

0^{\circ} C

than
that is water at

4^{\circ} C

2 Buoyancy will be more in water at

0^{\circ} C

than
that in water at

4^{\circ} C

3 Buoyancy in water at

0^{\circ} C

will be same as that in water at

4^{\circ} C

4 Buoyancy may be more or less in water

4^{\circ} C

depending on the radius of the sphere

Explanation:

A Buoyancy depends on the fluid in which the body is immersed. It depends upon the density of the fluid. Since density of water is maximum at $4^{\circ} C$ so the buoyancy at $4^{\circ} C$ will be maximum.

Karnataka CET-2019

Mechanical Properties of Fluids

143363 A vessel contains oil (density $ρ_{1}$ ) over a liquid of density $ρ_{2}$ . A homogeneous sphere of volume $V$ floats with half of its volume immersed in the liquid and the other half in oil. The weight of the sphere is

1

V (ρ_{2} - ρ_{1}) / 2

2

V (ρ_{2} + ρ_{1}) g / 2

3

V (ρ_{2} + ρ_{1})

4

V (ρ_{2} + ρ_{1}) / 2

Explanation:

B Weight of floating body $=$ Weight of liquid displaced
$W = ρ_{1} \times \frac{V}{2} \times g + ρ_{2} \times \frac{V}{2} \times g$
$= \frac{V (ρ_{1} + ρ_{2}) g}{2}$

NDA (I) 2010

Mechanical Properties of Fluids

143306 A spherical object of density $ρ$ is immersed in a fluid of density $σ$ . The object will move

1 downwards if

ρ > σ

2 downwards if

σ > ρ

3 upwards if

ρ < σ

4 upwards if

ρ > σ

Explanation:

A ,c) : If the density of object is greater than that of liquid $(ρ > σ)$ , then object will move downward,
If the density of object is lesser than that of liquid $(ρ <$ $σ$ ), then object move upward

UPSEE - 2011

Mechanical Properties of Fluids

143318 A ball floats on the surface of water in a container exposed to the atmosphere. When the container is covered and the air is partially removed, then the ball

1 rises

2 gets immersed more in water

3 remains immersed at its former depth

4 may rise or sink.

COMEDK 2020

Mechanical Properties of Fluids

143331 An aluminium sphere is dipped into water. Which of the following is true ?

1 Buoyancy will be less in water at

0^{\circ} C

than
that is water at

4^{\circ} C

2 Buoyancy will be more in water at

0^{\circ} C

than
that in water at

4^{\circ} C

3 Buoyancy in water at

0^{\circ} C

will be same as that in water at

4^{\circ} C

4 Buoyancy may be more or less in water

4^{\circ} C

depending on the radius of the sphere

Explanation:

A Buoyancy depends on the fluid in which the body is immersed. It depends upon the density of the fluid. Since density of water is maximum at $4^{\circ} C$ so the buoyancy at $4^{\circ} C$ will be maximum.

Karnataka CET-2019

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