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PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369685 When metal wire elongates by hanging load on it, then fractional change in volume $\frac{Δ V}{V}$ is proportional to

1

l Δ l

2

\frac{Δ l}{l}

3

\frac{2 Δ l}{l}

4

\sqrt{\frac{Δ l}{l}}

Explanation:

Poisson's ratio $σ = - \frac{Δ r / r}{Δ l / l}$
$\Rightarrow \frac{Δ V}{V} = \frac{Δ l}{l} (1 - 2 σ)$

PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369686 If compressibility of a material is $4 \times 10^{- 5}$ per $atm$ , pressure is $100 atm$ and volume is $100 c m^{3},$ then find the value of $Δ V$ .

1

0.4 c m^{3}

2

0.8 c m^{3}

3

0.6 c m^{3}

4

0.2 c m^{3}

Explanation:

Given, $β = 4 \times 10^{- 5}$ per atm,
$p = 100 atm$
and $V = 100 c m^{3}$
$= 100 \times 10^{- 6} m^{3}$
$∵$ Compressibility $=$ 1Bulk modulus of elasticity
$β = \frac{1}{Δ p \frac{V}{Δ V}} = \frac{Δ V}{Δ p V}$
$∴ Δ V = β (Δ p V) = 4 \times 10^{- 5} (100 \times 100 \times 10^{- 6})$
$= 0.4 \times 10^{- 6} m^{3} = 0.4 c m^{3}$

PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369687 Assertion :
Bulk modulus of elasticity represents incompressibility of the material.
Reason :
Bulk modulus of elasticity is proportional to change in pressure for a given volume-strain.

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.

Explanation:

Bulk modulus $B = \frac{- Δ P}{Δ V / V_{0}}$
Also, $B = \frac{1}{compressibility} (=$ In compressibility)
The bulk modulus measures a material's resistance to volume change under an applied pressure. For different materials, if $(\frac{Δ V}{V_{0}})$ is same, we have different values of $B$ with $B \propto (Δ P)$ . The reason correctly explains what bulk modulus represents. So correct option is (1).

PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369688 The order of bulk modulus for solids, liquids, and gases is

1

B_{solid} < B_{liquid} < B_{gas}

2

B_{solid} < B_{liquid} > B_{gas}

3

B_{solid} > B_{liquid} > B_{gas}

4 Cannot be predicted

Explanation:

Since solids are least compressible, $B_{solid}$ is highest.

PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369689 Assertion :
Gases have large compressibility.
Reason :
Compressibility is defined as the dfractional change in volume per unit decrease in pressure, which is high for gases.

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.

Explanation:

Molecules in gases are very poorly coupled to their neighbours molecules.
Since, compressibility is defined as the dfractional change in volume per unit increase or decrease in pressure.
$\begin{matrix} K = 1 / B \\ B = (\frac{- Δ P}{Δ V / V}) \end{matrix}$
Where, $B$ is bulk modulus and $Δ p$ change in pressure. So, in gases, dfractional change in volume with per unit increase or decrease in pressure is not very prominent. Thus, they have large compressibility.
Therefore, Assertion and Reason are correct and Reason is the correct explanation of Assertion.

PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369685 When metal wire elongates by hanging load on it, then fractional change in volume $\frac{Δ V}{V}$ is proportional to

1

l Δ l

2

\frac{Δ l}{l}

3

\frac{2 Δ l}{l}

4

\sqrt{\frac{Δ l}{l}}

Explanation:

Poisson's ratio $σ = - \frac{Δ r / r}{Δ l / l}$
$\Rightarrow \frac{Δ V}{V} = \frac{Δ l}{l} (1 - 2 σ)$

PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369686 If compressibility of a material is $4 \times 10^{- 5}$ per $atm$ , pressure is $100 atm$ and volume is $100 c m^{3},$ then find the value of $Δ V$ .

1

0.4 c m^{3}

2

0.8 c m^{3}

3

0.6 c m^{3}

4

0.2 c m^{3}

Explanation:

Given, $β = 4 \times 10^{- 5}$ per atm,
$p = 100 atm$
and $V = 100 c m^{3}$
$= 100 \times 10^{- 6} m^{3}$
$∵$ Compressibility $=$ 1Bulk modulus of elasticity
$β = \frac{1}{Δ p \frac{V}{Δ V}} = \frac{Δ V}{Δ p V}$
$∴ Δ V = β (Δ p V) = 4 \times 10^{- 5} (100 \times 100 \times 10^{- 6})$
$= 0.4 \times 10^{- 6} m^{3} = 0.4 c m^{3}$

PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369687 Assertion :
Bulk modulus of elasticity represents incompressibility of the material.
Reason :
Bulk modulus of elasticity is proportional to change in pressure for a given volume-strain.

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.

Explanation:

Bulk modulus $B = \frac{- Δ P}{Δ V / V_{0}}$
Also, $B = \frac{1}{compressibility} (=$ In compressibility)
The bulk modulus measures a material's resistance to volume change under an applied pressure. For different materials, if $(\frac{Δ V}{V_{0}})$ is same, we have different values of $B$ with $B \propto (Δ P)$ . The reason correctly explains what bulk modulus represents. So correct option is (1).

PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369688 The order of bulk modulus for solids, liquids, and gases is

1

B_{solid} < B_{liquid} < B_{gas}

2

B_{solid} < B_{liquid} > B_{gas}

3

B_{solid} > B_{liquid} > B_{gas}

4 Cannot be predicted

Explanation:

Since solids are least compressible, $B_{solid}$ is highest.

PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369689 Assertion :
Gases have large compressibility.
Reason :
Compressibility is defined as the dfractional change in volume per unit decrease in pressure, which is high for gases.

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.

Explanation:

Molecules in gases are very poorly coupled to their neighbours molecules.
Since, compressibility is defined as the dfractional change in volume per unit increase or decrease in pressure.
$\begin{matrix} K = 1 / B \\ B = (\frac{- Δ P}{Δ V / V}) \end{matrix}$
Where, $B$ is bulk modulus and $Δ p$ change in pressure. So, in gases, dfractional change in volume with per unit increase or decrease in pressure is not very prominent. Thus, they have large compressibility.
Therefore, Assertion and Reason are correct and Reason is the correct explanation of Assertion.

PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369685 When metal wire elongates by hanging load on it, then fractional change in volume $\frac{Δ V}{V}$ is proportional to

1

l Δ l

2

\frac{Δ l}{l}

3

\frac{2 Δ l}{l}

4

\sqrt{\frac{Δ l}{l}}

Explanation:

Poisson's ratio $σ = - \frac{Δ r / r}{Δ l / l}$
$\Rightarrow \frac{Δ V}{V} = \frac{Δ l}{l} (1 - 2 σ)$

PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369686 If compressibility of a material is $4 \times 10^{- 5}$ per $atm$ , pressure is $100 atm$ and volume is $100 c m^{3},$ then find the value of $Δ V$ .

1

0.4 c m^{3}

2

0.8 c m^{3}

3

0.6 c m^{3}

4

0.2 c m^{3}

Explanation:

Given, $β = 4 \times 10^{- 5}$ per atm,
$p = 100 atm$
and $V = 100 c m^{3}$
$= 100 \times 10^{- 6} m^{3}$
$∵$ Compressibility $=$ 1Bulk modulus of elasticity
$β = \frac{1}{Δ p \frac{V}{Δ V}} = \frac{Δ V}{Δ p V}$
$∴ Δ V = β (Δ p V) = 4 \times 10^{- 5} (100 \times 100 \times 10^{- 6})$
$= 0.4 \times 10^{- 6} m^{3} = 0.4 c m^{3}$

PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369687 Assertion :
Bulk modulus of elasticity represents incompressibility of the material.
Reason :
Bulk modulus of elasticity is proportional to change in pressure for a given volume-strain.

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.

Explanation:

Bulk modulus $B = \frac{- Δ P}{Δ V / V_{0}}$
Also, $B = \frac{1}{compressibility} (=$ In compressibility)
The bulk modulus measures a material's resistance to volume change under an applied pressure. For different materials, if $(\frac{Δ V}{V_{0}})$ is same, we have different values of $B$ with $B \propto (Δ P)$ . The reason correctly explains what bulk modulus represents. So correct option is (1).

PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369688 The order of bulk modulus for solids, liquids, and gases is

1

B_{solid} < B_{liquid} < B_{gas}

2

B_{solid} < B_{liquid} > B_{gas}

3

B_{solid} > B_{liquid} > B_{gas}

4 Cannot be predicted

Explanation:

Since solids are least compressible, $B_{solid}$ is highest.

PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369689 Assertion :
Gases have large compressibility.
Reason :
Compressibility is defined as the dfractional change in volume per unit decrease in pressure, which is high for gases.

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.

Explanation:

Molecules in gases are very poorly coupled to their neighbours molecules.
Since, compressibility is defined as the dfractional change in volume per unit increase or decrease in pressure.
$\begin{matrix} K = 1 / B \\ B = (\frac{- Δ P}{Δ V / V}) \end{matrix}$
Where, $B$ is bulk modulus and $Δ p$ change in pressure. So, in gases, dfractional change in volume with per unit increase or decrease in pressure is not very prominent. Thus, they have large compressibility.
Therefore, Assertion and Reason are correct and Reason is the correct explanation of Assertion.

PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369685 When metal wire elongates by hanging load on it, then fractional change in volume $\frac{Δ V}{V}$ is proportional to

1

l Δ l

2

\frac{Δ l}{l}

3

\frac{2 Δ l}{l}

4

\sqrt{\frac{Δ l}{l}}

Explanation:

Poisson's ratio $σ = - \frac{Δ r / r}{Δ l / l}$
$\Rightarrow \frac{Δ V}{V} = \frac{Δ l}{l} (1 - 2 σ)$

PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369686 If compressibility of a material is $4 \times 10^{- 5}$ per $atm$ , pressure is $100 atm$ and volume is $100 c m^{3},$ then find the value of $Δ V$ .

1

0.4 c m^{3}

2

0.8 c m^{3}

3

0.6 c m^{3}

4

0.2 c m^{3}

Explanation:

Given, $β = 4 \times 10^{- 5}$ per atm,
$p = 100 atm$
and $V = 100 c m^{3}$
$= 100 \times 10^{- 6} m^{3}$
$∵$ Compressibility $=$ 1Bulk modulus of elasticity
$β = \frac{1}{Δ p \frac{V}{Δ V}} = \frac{Δ V}{Δ p V}$
$∴ Δ V = β (Δ p V) = 4 \times 10^{- 5} (100 \times 100 \times 10^{- 6})$
$= 0.4 \times 10^{- 6} m^{3} = 0.4 c m^{3}$

PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369687 Assertion :
Bulk modulus of elasticity represents incompressibility of the material.
Reason :
Bulk modulus of elasticity is proportional to change in pressure for a given volume-strain.

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.

Explanation:

Bulk modulus $B = \frac{- Δ P}{Δ V / V_{0}}$
Also, $B = \frac{1}{compressibility} (=$ In compressibility)
The bulk modulus measures a material's resistance to volume change under an applied pressure. For different materials, if $(\frac{Δ V}{V_{0}})$ is same, we have different values of $B$ with $B \propto (Δ P)$ . The reason correctly explains what bulk modulus represents. So correct option is (1).

PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369688 The order of bulk modulus for solids, liquids, and gases is

1

B_{solid} < B_{liquid} < B_{gas}

2

B_{solid} < B_{liquid} > B_{gas}

3

B_{solid} > B_{liquid} > B_{gas}

4 Cannot be predicted

Explanation:

Since solids are least compressible, $B_{solid}$ is highest.

PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369689 Assertion :
Gases have large compressibility.
Reason :
Compressibility is defined as the dfractional change in volume per unit decrease in pressure, which is high for gases.

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.

Explanation:

Molecules in gases are very poorly coupled to their neighbours molecules.
Since, compressibility is defined as the dfractional change in volume per unit increase or decrease in pressure.
$\begin{matrix} K = 1 / B \\ B = (\frac{- Δ P}{Δ V / V}) \end{matrix}$
Where, $B$ is bulk modulus and $Δ p$ change in pressure. So, in gases, dfractional change in volume with per unit increase or decrease in pressure is not very prominent. Thus, they have large compressibility.
Therefore, Assertion and Reason are correct and Reason is the correct explanation of Assertion.

PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369685 When metal wire elongates by hanging load on it, then fractional change in volume $\frac{Δ V}{V}$ is proportional to

1

l Δ l

2

\frac{Δ l}{l}

3

\frac{2 Δ l}{l}

4

\sqrt{\frac{Δ l}{l}}

Explanation:

Poisson's ratio $σ = - \frac{Δ r / r}{Δ l / l}$
$\Rightarrow \frac{Δ V}{V} = \frac{Δ l}{l} (1 - 2 σ)$

PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369686 If compressibility of a material is $4 \times 10^{- 5}$ per $atm$ , pressure is $100 atm$ and volume is $100 c m^{3},$ then find the value of $Δ V$ .

1

0.4 c m^{3}

2

0.8 c m^{3}

3

0.6 c m^{3}

4

0.2 c m^{3}

Explanation:

Given, $β = 4 \times 10^{- 5}$ per atm,
$p = 100 atm$
and $V = 100 c m^{3}$
$= 100 \times 10^{- 6} m^{3}$
$∵$ Compressibility $=$ 1Bulk modulus of elasticity
$β = \frac{1}{Δ p \frac{V}{Δ V}} = \frac{Δ V}{Δ p V}$
$∴ Δ V = β (Δ p V) = 4 \times 10^{- 5} (100 \times 100 \times 10^{- 6})$
$= 0.4 \times 10^{- 6} m^{3} = 0.4 c m^{3}$

PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369687 Assertion :
Bulk modulus of elasticity represents incompressibility of the material.
Reason :
Bulk modulus of elasticity is proportional to change in pressure for a given volume-strain.

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.

Explanation:

Bulk modulus $B = \frac{- Δ P}{Δ V / V_{0}}$
Also, $B = \frac{1}{compressibility} (=$ In compressibility)
The bulk modulus measures a material's resistance to volume change under an applied pressure. For different materials, if $(\frac{Δ V}{V_{0}})$ is same, we have different values of $B$ with $B \propto (Δ P)$ . The reason correctly explains what bulk modulus represents. So correct option is (1).

PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369688 The order of bulk modulus for solids, liquids, and gases is

1

B_{solid} < B_{liquid} < B_{gas}

2

B_{solid} < B_{liquid} > B_{gas}

3

B_{solid} > B_{liquid} > B_{gas}

4 Cannot be predicted

Explanation:

Since solids are least compressible, $B_{solid}$ is highest.

PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369689 Assertion :
Gases have large compressibility.
Reason :
Compressibility is defined as the dfractional change in volume per unit decrease in pressure, which is high for gases.

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.

Explanation:

Molecules in gases are very poorly coupled to their neighbours molecules.
Since, compressibility is defined as the dfractional change in volume per unit increase or decrease in pressure.
$\begin{matrix} K = 1 / B \\ B = (\frac{- Δ P}{Δ V / V}) \end{matrix}$
Where, $B$ is bulk modulus and $Δ p$ change in pressure. So, in gases, dfractional change in volume with per unit increase or decrease in pressure is not very prominent. Thus, they have large compressibility.
Therefore, Assertion and Reason are correct and Reason is the correct explanation of Assertion.