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PHXI10:MECHANICAL PROPERTIES OF FLUIDS

360997 A metallic block weighs $15 N$ in air. It weighs $12 N$ when immersed in water and $13 N$ when immersed in another liquid. What is the specific gravity of the liquid?

1

1 / 3

2

2 / 3

3

12 / 13

4

13 / 15

Explanation:

Given that $m g = 15$
$\begin{aligned} m g - ρ_{w} V g = 12 \Rightarrow ρ_{w} V g = 3 \\ m g - ρ_{l} V g = 13 \Rightarrow ρ_{l} V g = 2 \\ \frac{ρ_{l}}{ρ_{w}} = \frac{2}{3} \end{aligned}$

PHXI10:MECHANICAL PROPERTIES OF FLUIDS

360998 A body weighs $50 g$ in air and $40 g$ in water. How much would it weigh in a liquid of specific gravity 2.5 ?

1

45 g

2

65 g

3

25 g

4

30 g

Explanation:

Given that $V \times ρ = 50; V (ρ - 1) = 40$
$\begin{aligned} \Rightarrow 50 - V = 40 \Rightarrow V = 10 c c; \\ \Rightarrow ρ = 5 g / c c, \end{aligned}$
Weight in a liquid of specific gravity
$= V (ρ - 2.5) \Rightarrow 10 (5 - 2.5) = 25 g m .$

PHXI10:MECHANICAL PROPERTIES OF FLUIDS

360999 A body is floating in liquid with $50 %$ of its volume outside the liquid. When the entire system accelerates upwards with an acceleration $g / 3$ . The percentage of its volume outside the liquid is

1

33 %

2

50 %

3

25.5 %

4

66 %

Explanation:

Let $V$ be volume of a body.
$ρ_{b}$ and $ρ_{l}$ be the density of the body and liquid respectively. When the body is floating in the liquid, then
Weight of the body $=$ Weight of the liquid displaced
$V ρ_{b} g = V_{i n} ρ_{l} g$
$\frac{V_{i n}}{V} = \frac{ρ_{b}}{ρ_{l}} (1)$
$∴$ Volume of the body outside the liquid is
$V_{o u t} = V - V_{i n} = V - V \frac{ρ_{b}}{ρ_{l}} [U s i n g (1)]$
$= V (1 - \frac{ρ_{b}}{ρ_{l}})$
$∴ \frac{Volume of the body out side the liquid}{Volume of the body}$
$= (1 - \frac{ρ_{b}}{ρ_{1}})$
As this ratio is independent of the effective value of acceleration due to gravity, so the percentage of the volume of the body outside the liquid will remain unchanged.

PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361000 A balloon has volume of $1000 m^{3}$ . It is filled with hydrogen $(ρ = 0.09 g / L)$ . If the density of air is $1.29 g / L$ , it can lift a total weight of

1

600 k g

2

1200 k g

3

300 k g

4

1800 k g

Explanation:

$1 g / L = 1 k g / m^{3}$
Upthrust $=$ total downward force
$∴ 1000 \times 1.29 \times g = (1000 \times 0.09 \times g + m g)$
$∴ m = 1200 k g$

PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361001 A jar is filled with two non-mixing liquids 1 and 2 having densities $ρ_{1}$ and $ρ_{2}$ , respectively. A solid ball made of material of density $ρ_{3}$ , is dropped in the jar. It comes to equilibrium in the position shown in the figure. Which of the following is true for $ρ_{1}, ρ_{2}$ and $ρ_{3}$ ?
supporting img

1

ρ_{3} < ρ_{1} < ρ_{2}

2

ρ_{1} > ρ_{3} > ρ_{2}

3

ρ_{1} < ρ_{2} < ρ_{3}

4

ρ_{1} < ρ_{3} < ρ_{2}

Explanation:

As liquid 2 is present below the liquid 1
then
$ρ_{2} > ρ_{1} (1)$
As ball of density $ρ_{3}$ is floating in liquid of
density $ρ_{1}$ ]
$ρ_{1} > ρ_{3} (2)$
From eqn. (1) and (2)
$ρ_{3} < ρ_{1} < ρ_{2}$

PHXI10:MECHANICAL PROPERTIES OF FLUIDS

360997 A metallic block weighs $15 N$ in air. It weighs $12 N$ when immersed in water and $13 N$ when immersed in another liquid. What is the specific gravity of the liquid?

1

1 / 3

2

2 / 3

3

12 / 13

4

13 / 15

Explanation:

Given that $m g = 15$
$\begin{aligned} m g - ρ_{w} V g = 12 \Rightarrow ρ_{w} V g = 3 \\ m g - ρ_{l} V g = 13 \Rightarrow ρ_{l} V g = 2 \\ \frac{ρ_{l}}{ρ_{w}} = \frac{2}{3} \end{aligned}$

PHXI10:MECHANICAL PROPERTIES OF FLUIDS

360998 A body weighs $50 g$ in air and $40 g$ in water. How much would it weigh in a liquid of specific gravity 2.5 ?

1

45 g

2

65 g

3

25 g

4

30 g

Explanation:

Given that $V \times ρ = 50; V (ρ - 1) = 40$
$\begin{aligned} \Rightarrow 50 - V = 40 \Rightarrow V = 10 c c; \\ \Rightarrow ρ = 5 g / c c, \end{aligned}$
Weight in a liquid of specific gravity
$= V (ρ - 2.5) \Rightarrow 10 (5 - 2.5) = 25 g m .$

PHXI10:MECHANICAL PROPERTIES OF FLUIDS

360999 A body is floating in liquid with $50 %$ of its volume outside the liquid. When the entire system accelerates upwards with an acceleration $g / 3$ . The percentage of its volume outside the liquid is

1

33 %

2

50 %

3

25.5 %

4

66 %

Explanation:

Let $V$ be volume of a body.
$ρ_{b}$ and $ρ_{l}$ be the density of the body and liquid respectively. When the body is floating in the liquid, then
Weight of the body $=$ Weight of the liquid displaced
$V ρ_{b} g = V_{i n} ρ_{l} g$
$\frac{V_{i n}}{V} = \frac{ρ_{b}}{ρ_{l}} (1)$
$∴$ Volume of the body outside the liquid is
$V_{o u t} = V - V_{i n} = V - V \frac{ρ_{b}}{ρ_{l}} [U s i n g (1)]$
$= V (1 - \frac{ρ_{b}}{ρ_{l}})$
$∴ \frac{Volume of the body out side the liquid}{Volume of the body}$
$= (1 - \frac{ρ_{b}}{ρ_{1}})$
As this ratio is independent of the effective value of acceleration due to gravity, so the percentage of the volume of the body outside the liquid will remain unchanged.

PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361000 A balloon has volume of $1000 m^{3}$ . It is filled with hydrogen $(ρ = 0.09 g / L)$ . If the density of air is $1.29 g / L$ , it can lift a total weight of

1

600 k g

2

1200 k g

3

300 k g

4

1800 k g

Explanation:

$1 g / L = 1 k g / m^{3}$
Upthrust $=$ total downward force
$∴ 1000 \times 1.29 \times g = (1000 \times 0.09 \times g + m g)$
$∴ m = 1200 k g$

PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361001 A jar is filled with two non-mixing liquids 1 and 2 having densities $ρ_{1}$ and $ρ_{2}$ , respectively. A solid ball made of material of density $ρ_{3}$ , is dropped in the jar. It comes to equilibrium in the position shown in the figure. Which of the following is true for $ρ_{1}, ρ_{2}$ and $ρ_{3}$ ?
supporting img

1

ρ_{3} < ρ_{1} < ρ_{2}

2

ρ_{1} > ρ_{3} > ρ_{2}

3

ρ_{1} < ρ_{2} < ρ_{3}

4

ρ_{1} < ρ_{3} < ρ_{2}

Explanation:

As liquid 2 is present below the liquid 1
then
$ρ_{2} > ρ_{1} (1)$
As ball of density $ρ_{3}$ is floating in liquid of
density $ρ_{1}$ ]
$ρ_{1} > ρ_{3} (2)$
From eqn. (1) and (2)
$ρ_{3} < ρ_{1} < ρ_{2}$

PHXI10:MECHANICAL PROPERTIES OF FLUIDS

360997 A metallic block weighs $15 N$ in air. It weighs $12 N$ when immersed in water and $13 N$ when immersed in another liquid. What is the specific gravity of the liquid?

1

1 / 3

2

2 / 3

3

12 / 13

4

13 / 15

Explanation:

Given that $m g = 15$
$\begin{aligned} m g - ρ_{w} V g = 12 \Rightarrow ρ_{w} V g = 3 \\ m g - ρ_{l} V g = 13 \Rightarrow ρ_{l} V g = 2 \\ \frac{ρ_{l}}{ρ_{w}} = \frac{2}{3} \end{aligned}$

PHXI10:MECHANICAL PROPERTIES OF FLUIDS

360998 A body weighs $50 g$ in air and $40 g$ in water. How much would it weigh in a liquid of specific gravity 2.5 ?

1

45 g

2

65 g

3

25 g

4

30 g

Explanation:

Given that $V \times ρ = 50; V (ρ - 1) = 40$
$\begin{aligned} \Rightarrow 50 - V = 40 \Rightarrow V = 10 c c; \\ \Rightarrow ρ = 5 g / c c, \end{aligned}$
Weight in a liquid of specific gravity
$= V (ρ - 2.5) \Rightarrow 10 (5 - 2.5) = 25 g m .$

PHXI10:MECHANICAL PROPERTIES OF FLUIDS

360999 A body is floating in liquid with $50 %$ of its volume outside the liquid. When the entire system accelerates upwards with an acceleration $g / 3$ . The percentage of its volume outside the liquid is

1

33 %

2

50 %

3

25.5 %

4

66 %

Explanation:

Let $V$ be volume of a body.
$ρ_{b}$ and $ρ_{l}$ be the density of the body and liquid respectively. When the body is floating in the liquid, then
Weight of the body $=$ Weight of the liquid displaced
$V ρ_{b} g = V_{i n} ρ_{l} g$
$\frac{V_{i n}}{V} = \frac{ρ_{b}}{ρ_{l}} (1)$
$∴$ Volume of the body outside the liquid is
$V_{o u t} = V - V_{i n} = V - V \frac{ρ_{b}}{ρ_{l}} [U s i n g (1)]$
$= V (1 - \frac{ρ_{b}}{ρ_{l}})$
$∴ \frac{Volume of the body out side the liquid}{Volume of the body}$
$= (1 - \frac{ρ_{b}}{ρ_{1}})$
As this ratio is independent of the effective value of acceleration due to gravity, so the percentage of the volume of the body outside the liquid will remain unchanged.

PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361000 A balloon has volume of $1000 m^{3}$ . It is filled with hydrogen $(ρ = 0.09 g / L)$ . If the density of air is $1.29 g / L$ , it can lift a total weight of

1

600 k g

2

1200 k g

3

300 k g

4

1800 k g

Explanation:

$1 g / L = 1 k g / m^{3}$
Upthrust $=$ total downward force
$∴ 1000 \times 1.29 \times g = (1000 \times 0.09 \times g + m g)$
$∴ m = 1200 k g$

PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361001 A jar is filled with two non-mixing liquids 1 and 2 having densities $ρ_{1}$ and $ρ_{2}$ , respectively. A solid ball made of material of density $ρ_{3}$ , is dropped in the jar. It comes to equilibrium in the position shown in the figure. Which of the following is true for $ρ_{1}, ρ_{2}$ and $ρ_{3}$ ?
supporting img

1

ρ_{3} < ρ_{1} < ρ_{2}

2

ρ_{1} > ρ_{3} > ρ_{2}

3

ρ_{1} < ρ_{2} < ρ_{3}

4

ρ_{1} < ρ_{3} < ρ_{2}

Explanation:

As liquid 2 is present below the liquid 1
then
$ρ_{2} > ρ_{1} (1)$
As ball of density $ρ_{3}$ is floating in liquid of
density $ρ_{1}$ ]
$ρ_{1} > ρ_{3} (2)$
From eqn. (1) and (2)
$ρ_{3} < ρ_{1} < ρ_{2}$

PHXI10:MECHANICAL PROPERTIES OF FLUIDS

360997 A metallic block weighs $15 N$ in air. It weighs $12 N$ when immersed in water and $13 N$ when immersed in another liquid. What is the specific gravity of the liquid?

1

1 / 3

2

2 / 3

3

12 / 13

4

13 / 15

Explanation:

Given that $m g = 15$
$\begin{aligned} m g - ρ_{w} V g = 12 \Rightarrow ρ_{w} V g = 3 \\ m g - ρ_{l} V g = 13 \Rightarrow ρ_{l} V g = 2 \\ \frac{ρ_{l}}{ρ_{w}} = \frac{2}{3} \end{aligned}$

PHXI10:MECHANICAL PROPERTIES OF FLUIDS

360998 A body weighs $50 g$ in air and $40 g$ in water. How much would it weigh in a liquid of specific gravity 2.5 ?

1

45 g

2

65 g

3

25 g

4

30 g

Explanation:

Given that $V \times ρ = 50; V (ρ - 1) = 40$
$\begin{aligned} \Rightarrow 50 - V = 40 \Rightarrow V = 10 c c; \\ \Rightarrow ρ = 5 g / c c, \end{aligned}$
Weight in a liquid of specific gravity
$= V (ρ - 2.5) \Rightarrow 10 (5 - 2.5) = 25 g m .$

PHXI10:MECHANICAL PROPERTIES OF FLUIDS

360999 A body is floating in liquid with $50 %$ of its volume outside the liquid. When the entire system accelerates upwards with an acceleration $g / 3$ . The percentage of its volume outside the liquid is

1

33 %

2

50 %

3

25.5 %

4

66 %

Explanation:

Let $V$ be volume of a body.
$ρ_{b}$ and $ρ_{l}$ be the density of the body and liquid respectively. When the body is floating in the liquid, then
Weight of the body $=$ Weight of the liquid displaced
$V ρ_{b} g = V_{i n} ρ_{l} g$
$\frac{V_{i n}}{V} = \frac{ρ_{b}}{ρ_{l}} (1)$
$∴$ Volume of the body outside the liquid is
$V_{o u t} = V - V_{i n} = V - V \frac{ρ_{b}}{ρ_{l}} [U s i n g (1)]$
$= V (1 - \frac{ρ_{b}}{ρ_{l}})$
$∴ \frac{Volume of the body out side the liquid}{Volume of the body}$
$= (1 - \frac{ρ_{b}}{ρ_{1}})$
As this ratio is independent of the effective value of acceleration due to gravity, so the percentage of the volume of the body outside the liquid will remain unchanged.

PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361000 A balloon has volume of $1000 m^{3}$ . It is filled with hydrogen $(ρ = 0.09 g / L)$ . If the density of air is $1.29 g / L$ , it can lift a total weight of

1

600 k g

2

1200 k g

3

300 k g

4

1800 k g

Explanation:

$1 g / L = 1 k g / m^{3}$
Upthrust $=$ total downward force
$∴ 1000 \times 1.29 \times g = (1000 \times 0.09 \times g + m g)$
$∴ m = 1200 k g$

PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361001 A jar is filled with two non-mixing liquids 1 and 2 having densities $ρ_{1}$ and $ρ_{2}$ , respectively. A solid ball made of material of density $ρ_{3}$ , is dropped in the jar. It comes to equilibrium in the position shown in the figure. Which of the following is true for $ρ_{1}, ρ_{2}$ and $ρ_{3}$ ?
supporting img

1

ρ_{3} < ρ_{1} < ρ_{2}

2

ρ_{1} > ρ_{3} > ρ_{2}

3

ρ_{1} < ρ_{2} < ρ_{3}

4

ρ_{1} < ρ_{3} < ρ_{2}

Explanation:

As liquid 2 is present below the liquid 1
then
$ρ_{2} > ρ_{1} (1)$
As ball of density $ρ_{3}$ is floating in liquid of
density $ρ_{1}$ ]
$ρ_{1} > ρ_{3} (2)$
From eqn. (1) and (2)
$ρ_{3} < ρ_{1} < ρ_{2}$

PHXI10:MECHANICAL PROPERTIES OF FLUIDS

360997 A metallic block weighs $15 N$ in air. It weighs $12 N$ when immersed in water and $13 N$ when immersed in another liquid. What is the specific gravity of the liquid?

1

1 / 3

2

2 / 3

3

12 / 13

4

13 / 15

Explanation:

Given that $m g = 15$
$\begin{aligned} m g - ρ_{w} V g = 12 \Rightarrow ρ_{w} V g = 3 \\ m g - ρ_{l} V g = 13 \Rightarrow ρ_{l} V g = 2 \\ \frac{ρ_{l}}{ρ_{w}} = \frac{2}{3} \end{aligned}$

PHXI10:MECHANICAL PROPERTIES OF FLUIDS

360998 A body weighs $50 g$ in air and $40 g$ in water. How much would it weigh in a liquid of specific gravity 2.5 ?

1

45 g

2

65 g

3

25 g

4

30 g

Explanation:

Given that $V \times ρ = 50; V (ρ - 1) = 40$
$\begin{aligned} \Rightarrow 50 - V = 40 \Rightarrow V = 10 c c; \\ \Rightarrow ρ = 5 g / c c, \end{aligned}$
Weight in a liquid of specific gravity
$= V (ρ - 2.5) \Rightarrow 10 (5 - 2.5) = 25 g m .$

PHXI10:MECHANICAL PROPERTIES OF FLUIDS

360999 A body is floating in liquid with $50 %$ of its volume outside the liquid. When the entire system accelerates upwards with an acceleration $g / 3$ . The percentage of its volume outside the liquid is

1

33 %

2

50 %

3

25.5 %

4

66 %

Explanation:

Let $V$ be volume of a body.
$ρ_{b}$ and $ρ_{l}$ be the density of the body and liquid respectively. When the body is floating in the liquid, then
Weight of the body $=$ Weight of the liquid displaced
$V ρ_{b} g = V_{i n} ρ_{l} g$
$\frac{V_{i n}}{V} = \frac{ρ_{b}}{ρ_{l}} (1)$
$∴$ Volume of the body outside the liquid is
$V_{o u t} = V - V_{i n} = V - V \frac{ρ_{b}}{ρ_{l}} [U s i n g (1)]$
$= V (1 - \frac{ρ_{b}}{ρ_{l}})$
$∴ \frac{Volume of the body out side the liquid}{Volume of the body}$
$= (1 - \frac{ρ_{b}}{ρ_{1}})$
As this ratio is independent of the effective value of acceleration due to gravity, so the percentage of the volume of the body outside the liquid will remain unchanged.

PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361000 A balloon has volume of $1000 m^{3}$ . It is filled with hydrogen $(ρ = 0.09 g / L)$ . If the density of air is $1.29 g / L$ , it can lift a total weight of

1

600 k g

2

1200 k g

3

300 k g

4

1800 k g

Explanation:

$1 g / L = 1 k g / m^{3}$
Upthrust $=$ total downward force
$∴ 1000 \times 1.29 \times g = (1000 \times 0.09 \times g + m g)$
$∴ m = 1200 k g$

PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361001 A jar is filled with two non-mixing liquids 1 and 2 having densities $ρ_{1}$ and $ρ_{2}$ , respectively. A solid ball made of material of density $ρ_{3}$ , is dropped in the jar. It comes to equilibrium in the position shown in the figure. Which of the following is true for $ρ_{1}, ρ_{2}$ and $ρ_{3}$ ?
supporting img

1

ρ_{3} < ρ_{1} < ρ_{2}

2

ρ_{1} > ρ_{3} > ρ_{2}

3

ρ_{1} < ρ_{2} < ρ_{3}

4

ρ_{1} < ρ_{3} < ρ_{2}

Explanation:

As liquid 2 is present below the liquid 1
then
$ρ_{2} > ρ_{1} (1)$
As ball of density $ρ_{3}$ is floating in liquid of
density $ρ_{1}$ ]
$ρ_{1} > ρ_{3} (2)$
From eqn. (1) and (2)
$ρ_{3} < ρ_{1} < ρ_{2}$

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