QBManager

PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361027 A block of silver of mass $4 k g$ hanging from a string is immersed in a liquid of relative density 1.0. If relative density of silver is 10 , then tension in the string will be:[Take $g = 10 m / s^{2}$ ]

1

36 N

2

73 N

3

42 N

4

21 N

Explanation:

The weight is balanced by upward buoyancy force and tension.
$\begin{aligned} T + F_{b} = m g \\ T + ρ_{l} V g = m g \\ T + ρ_{l} \frac{m}{ρ} g = m g \\ T + (1.0) ρ_{W} \frac{m}{10 ρ_{W}} 10 = 4 \times 10 \\ T = 36 N \end{aligned}$

PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361028 A hemispherical portion of radius $R$ is removed from the bottom of a cylinder of radius $R$ . The volume of the remaining cylinder is $V$ and its mass $M$ . It is suspended by a string in a liquid of density $ρ$ where it stays vertical. The upper surface of the cylinder is at a depth $h$ below the liquid surface. The force on the bottom of the cylinder by the liquid is:
supporting img

1

M g - V ρ g

2

M g

3

ρ g (V + π R^{2} h)

4

M g + π R^{2} h ρ g

Explanation:

Let $F_{b} (= ρ V g)$ is the buoyancy force on the cylinder. Let $F$ is the pressure force exerted by the liquid on the base of the cylinder.
From the definition of buoyancy force
$\begin{aligned} F_{b} = F - π R^{2} ρ g h \\ ρ V g = F - π R^{2} ρ g h \\ \Rightarrow F = ρ g V + π R^{2} ρ g h \end{aligned}$

PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361029 When a body is fully immersed in a liquid, the loss of weight of the body is equal to

1 Apparent weight of the body

2 Force of buoyancy

3 Half the force of buoyancy

4 Twice the force of buoyancy

PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361030 Assertion :
A hydrogen filled balloon stops rising after it has attained a certain height in the sky.
Reason :
The atmospheric pressure decreases with height.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.

2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.

3 Assertion is correct but Reason is incorrect.

4 Assertion is incorrect but reason is correct.

PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361031 A raft of mass $M = 600 k g$ floats in calm water with $7 c m$ submerged. When a man stands on the raft, $8.4 c m$ are submerged, the man's mass is

1

30 k g

2

60 k g

3

90 k g

4

120 k g

Explanation:

Upthrust on $7 c m = 600 k g$
$∴$ Upthrusty on further $1.4 c m = \frac{600}{7} \times 1.4 = 120 k g$

PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361027 A block of silver of mass $4 k g$ hanging from a string is immersed in a liquid of relative density 1.0. If relative density of silver is 10 , then tension in the string will be:[Take $g = 10 m / s^{2}$ ]

1

36 N

2

73 N

3

42 N

4

21 N

Explanation:

The weight is balanced by upward buoyancy force and tension.
$\begin{aligned} T + F_{b} = m g \\ T + ρ_{l} V g = m g \\ T + ρ_{l} \frac{m}{ρ} g = m g \\ T + (1.0) ρ_{W} \frac{m}{10 ρ_{W}} 10 = 4 \times 10 \\ T = 36 N \end{aligned}$

PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361028 A hemispherical portion of radius $R$ is removed from the bottom of a cylinder of radius $R$ . The volume of the remaining cylinder is $V$ and its mass $M$ . It is suspended by a string in a liquid of density $ρ$ where it stays vertical. The upper surface of the cylinder is at a depth $h$ below the liquid surface. The force on the bottom of the cylinder by the liquid is:
supporting img

1

M g - V ρ g

2

M g

3

ρ g (V + π R^{2} h)

4

M g + π R^{2} h ρ g

Explanation:

Let $F_{b} (= ρ V g)$ is the buoyancy force on the cylinder. Let $F$ is the pressure force exerted by the liquid on the base of the cylinder.
From the definition of buoyancy force
$\begin{aligned} F_{b} = F - π R^{2} ρ g h \\ ρ V g = F - π R^{2} ρ g h \\ \Rightarrow F = ρ g V + π R^{2} ρ g h \end{aligned}$

PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361029 When a body is fully immersed in a liquid, the loss of weight of the body is equal to

1 Apparent weight of the body

2 Force of buoyancy

3 Half the force of buoyancy

4 Twice the force of buoyancy

PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361030 Assertion :
A hydrogen filled balloon stops rising after it has attained a certain height in the sky.
Reason :
The atmospheric pressure decreases with height.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.

2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.

3 Assertion is correct but Reason is incorrect.

4 Assertion is incorrect but reason is correct.

PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361031 A raft of mass $M = 600 k g$ floats in calm water with $7 c m$ submerged. When a man stands on the raft, $8.4 c m$ are submerged, the man's mass is

1

30 k g

2

60 k g

3

90 k g

4

120 k g

Explanation:

Upthrust on $7 c m = 600 k g$
$∴$ Upthrusty on further $1.4 c m = \frac{600}{7} \times 1.4 = 120 k g$

PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361027 A block of silver of mass $4 k g$ hanging from a string is immersed in a liquid of relative density 1.0. If relative density of silver is 10 , then tension in the string will be:[Take $g = 10 m / s^{2}$ ]

1

36 N

2

73 N

3

42 N

4

21 N

Explanation:

The weight is balanced by upward buoyancy force and tension.
$\begin{aligned} T + F_{b} = m g \\ T + ρ_{l} V g = m g \\ T + ρ_{l} \frac{m}{ρ} g = m g \\ T + (1.0) ρ_{W} \frac{m}{10 ρ_{W}} 10 = 4 \times 10 \\ T = 36 N \end{aligned}$

PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361028 A hemispherical portion of radius $R$ is removed from the bottom of a cylinder of radius $R$ . The volume of the remaining cylinder is $V$ and its mass $M$ . It is suspended by a string in a liquid of density $ρ$ where it stays vertical. The upper surface of the cylinder is at a depth $h$ below the liquid surface. The force on the bottom of the cylinder by the liquid is:
supporting img

1

M g - V ρ g

2

M g

3

ρ g (V + π R^{2} h)

4

M g + π R^{2} h ρ g

Explanation:

Let $F_{b} (= ρ V g)$ is the buoyancy force on the cylinder. Let $F$ is the pressure force exerted by the liquid on the base of the cylinder.
From the definition of buoyancy force
$\begin{aligned} F_{b} = F - π R^{2} ρ g h \\ ρ V g = F - π R^{2} ρ g h \\ \Rightarrow F = ρ g V + π R^{2} ρ g h \end{aligned}$

PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361029 When a body is fully immersed in a liquid, the loss of weight of the body is equal to

1 Apparent weight of the body

2 Force of buoyancy

3 Half the force of buoyancy

4 Twice the force of buoyancy

PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361030 Assertion :
A hydrogen filled balloon stops rising after it has attained a certain height in the sky.
Reason :
The atmospheric pressure decreases with height.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.

2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.

3 Assertion is correct but Reason is incorrect.

4 Assertion is incorrect but reason is correct.

PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361031 A raft of mass $M = 600 k g$ floats in calm water with $7 c m$ submerged. When a man stands on the raft, $8.4 c m$ are submerged, the man's mass is

1

30 k g

2

60 k g

3

90 k g

4

120 k g

Explanation:

Upthrust on $7 c m = 600 k g$
$∴$ Upthrusty on further $1.4 c m = \frac{600}{7} \times 1.4 = 120 k g$

PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361027 A block of silver of mass $4 k g$ hanging from a string is immersed in a liquid of relative density 1.0. If relative density of silver is 10 , then tension in the string will be:[Take $g = 10 m / s^{2}$ ]

1

36 N

2

73 N

3

42 N

4

21 N

Explanation:

The weight is balanced by upward buoyancy force and tension.
$\begin{aligned} T + F_{b} = m g \\ T + ρ_{l} V g = m g \\ T + ρ_{l} \frac{m}{ρ} g = m g \\ T + (1.0) ρ_{W} \frac{m}{10 ρ_{W}} 10 = 4 \times 10 \\ T = 36 N \end{aligned}$

PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361028 A hemispherical portion of radius $R$ is removed from the bottom of a cylinder of radius $R$ . The volume of the remaining cylinder is $V$ and its mass $M$ . It is suspended by a string in a liquid of density $ρ$ where it stays vertical. The upper surface of the cylinder is at a depth $h$ below the liquid surface. The force on the bottom of the cylinder by the liquid is:
supporting img

1

M g - V ρ g

2

M g

3

ρ g (V + π R^{2} h)

4

M g + π R^{2} h ρ g

Explanation:

Let $F_{b} (= ρ V g)$ is the buoyancy force on the cylinder. Let $F$ is the pressure force exerted by the liquid on the base of the cylinder.
From the definition of buoyancy force
$\begin{aligned} F_{b} = F - π R^{2} ρ g h \\ ρ V g = F - π R^{2} ρ g h \\ \Rightarrow F = ρ g V + π R^{2} ρ g h \end{aligned}$

PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361029 When a body is fully immersed in a liquid, the loss of weight of the body is equal to

1 Apparent weight of the body

2 Force of buoyancy

3 Half the force of buoyancy

4 Twice the force of buoyancy

PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361030 Assertion :
A hydrogen filled balloon stops rising after it has attained a certain height in the sky.
Reason :
The atmospheric pressure decreases with height.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.

2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.

3 Assertion is correct but Reason is incorrect.

4 Assertion is incorrect but reason is correct.

PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361031 A raft of mass $M = 600 k g$ floats in calm water with $7 c m$ submerged. When a man stands on the raft, $8.4 c m$ are submerged, the man's mass is

1

30 k g

2

60 k g

3

90 k g

4

120 k g

Explanation:

Upthrust on $7 c m = 600 k g$
$∴$ Upthrusty on further $1.4 c m = \frac{600}{7} \times 1.4 = 120 k g$

PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361027 A block of silver of mass $4 k g$ hanging from a string is immersed in a liquid of relative density 1.0. If relative density of silver is 10 , then tension in the string will be:[Take $g = 10 m / s^{2}$ ]

1

36 N

2

73 N

3

42 N

4

21 N

Explanation:

The weight is balanced by upward buoyancy force and tension.
$\begin{aligned} T + F_{b} = m g \\ T + ρ_{l} V g = m g \\ T + ρ_{l} \frac{m}{ρ} g = m g \\ T + (1.0) ρ_{W} \frac{m}{10 ρ_{W}} 10 = 4 \times 10 \\ T = 36 N \end{aligned}$

PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361028 A hemispherical portion of radius $R$ is removed from the bottom of a cylinder of radius $R$ . The volume of the remaining cylinder is $V$ and its mass $M$ . It is suspended by a string in a liquid of density $ρ$ where it stays vertical. The upper surface of the cylinder is at a depth $h$ below the liquid surface. The force on the bottom of the cylinder by the liquid is:
supporting img

1

M g - V ρ g

2

M g

3

ρ g (V + π R^{2} h)

4

M g + π R^{2} h ρ g

Explanation:

Let $F_{b} (= ρ V g)$ is the buoyancy force on the cylinder. Let $F$ is the pressure force exerted by the liquid on the base of the cylinder.
From the definition of buoyancy force
$\begin{aligned} F_{b} = F - π R^{2} ρ g h \\ ρ V g = F - π R^{2} ρ g h \\ \Rightarrow F = ρ g V + π R^{2} ρ g h \end{aligned}$

PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361029 When a body is fully immersed in a liquid, the loss of weight of the body is equal to

1 Apparent weight of the body

2 Force of buoyancy

3 Half the force of buoyancy

4 Twice the force of buoyancy

PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361030 Assertion :
A hydrogen filled balloon stops rising after it has attained a certain height in the sky.
Reason :
The atmospheric pressure decreases with height.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.

2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.

3 Assertion is correct but Reason is incorrect.

4 Assertion is incorrect but reason is correct.

PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361031 A raft of mass $M = 600 k g$ floats in calm water with $7 c m$ submerged. When a man stands on the raft, $8.4 c m$ are submerged, the man's mass is

1

30 k g

2

60 k g

3

90 k g

4

120 k g

Explanation:

Upthrust on $7 c m = 600 k g$
$∴$ Upthrusty on further $1.4 c m = \frac{600}{7} \times 1.4 = 120 k g$