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Mechanical Properties of Solids

140895 A copper wire and a steel wire of the same diameter and length are joined end to end and a force is applied which stretches their combined length by $1 cm$ . Then, the two wires will have

1 the same stress and strain

2 the same stress but different strains

3 the same strain but different stresses

4 different stresses and strains

Manipal UGET-2012

Mechanical Properties of Solids

140897 The pressure applied from all directions on a cube is p. How much its temperature should be raised to maintain the original volume? The volume elasticity of the cube is $β$ and the coefficient of volume expansion is $α$ .

1

\frac{p}{α β}

2

\frac{p α}{β}

3

\frac{p β}{α}

4

\frac{α β}{p}

Explanation:

A If coefficient of volume expansion is $α$ and rise in temperature is $Δ θ$ , then $Δ V = V α Δ θ$
$\frac{Δ V}{V} = α Δ θ$
$∴$ Volume elasticity $(β) = \frac{Stress}{Strain}$
$= \frac{P}{α Δ θ}$
$Δ θ = \frac{p}{α β}$

Mechanical Properties of Solids

140912 The elastic energy stored per unit volume in a stretched wire is

1

\frac{1}{2}

(Young modulus

) (Strain)^{2}

2

\frac{1}{2} (

Stress

) (Strain)^{2}

3

\frac{1}{2} \frac{Stress}{Strain}

4

\frac{1}{2}

(Young modulus) (Stress)

Explanation:

A Energy stored per unit volume.
$E = \frac{1}{2} \times stress \times strain$
We know that,
$Strain = \frac{stress}{Young's modulus (Y)}$
$E = \frac{1}{2} \times Y \times (strain)^{2}$

J and K CET- 2010

Mechanical Properties of Solids

140915 If longitudinal strain for a wire is 0.03 and its Poisson's ratio is 0.5 , then its lateral strain is

1 0.003

2 0.0075

3 0.015

4 0.4

Explanation:

C Poisson 's ratio $= - \frac{lateral strain}{longitudinal strain}$
Longitudinal strain for wire in 0.03 and poisson ratio is 0.5 .
$0.5 = - \frac{lateral strain}{0.03}$
Lateral strain $= - 0.015$
[Negative sign shows decrease in dimension in lateral direction.]

J and K CET- 2006

Mechanical Properties of Solids

140895 A copper wire and a steel wire of the same diameter and length are joined end to end and a force is applied which stretches their combined length by $1 cm$ . Then, the two wires will have

1 the same stress and strain

2 the same stress but different strains

3 the same strain but different stresses

4 different stresses and strains

Manipal UGET-2012

Mechanical Properties of Solids

140897 The pressure applied from all directions on a cube is p. How much its temperature should be raised to maintain the original volume? The volume elasticity of the cube is $β$ and the coefficient of volume expansion is $α$ .

1

\frac{p}{α β}

2

\frac{p α}{β}

3

\frac{p β}{α}

4

\frac{α β}{p}

Explanation:

A If coefficient of volume expansion is $α$ and rise in temperature is $Δ θ$ , then $Δ V = V α Δ θ$
$\frac{Δ V}{V} = α Δ θ$
$∴$ Volume elasticity $(β) = \frac{Stress}{Strain}$
$= \frac{P}{α Δ θ}$
$Δ θ = \frac{p}{α β}$

Mechanical Properties of Solids

140912 The elastic energy stored per unit volume in a stretched wire is

1

\frac{1}{2}

(Young modulus

) (Strain)^{2}

2

\frac{1}{2} (

Stress

) (Strain)^{2}

3

\frac{1}{2} \frac{Stress}{Strain}

4

\frac{1}{2}

(Young modulus) (Stress)

Explanation:

A Energy stored per unit volume.
$E = \frac{1}{2} \times stress \times strain$
We know that,
$Strain = \frac{stress}{Young's modulus (Y)}$
$E = \frac{1}{2} \times Y \times (strain)^{2}$

J and K CET- 2010

Mechanical Properties of Solids

140915 If longitudinal strain for a wire is 0.03 and its Poisson's ratio is 0.5 , then its lateral strain is

1 0.003

2 0.0075

3 0.015

4 0.4

Explanation:

C Poisson 's ratio $= - \frac{lateral strain}{longitudinal strain}$
Longitudinal strain for wire in 0.03 and poisson ratio is 0.5 .
$0.5 = - \frac{lateral strain}{0.03}$
Lateral strain $= - 0.015$
[Negative sign shows decrease in dimension in lateral direction.]

J and K CET- 2006

Mechanical Properties of Solids

140895 A copper wire and a steel wire of the same diameter and length are joined end to end and a force is applied which stretches their combined length by $1 cm$ . Then, the two wires will have

1 the same stress and strain

2 the same stress but different strains

3 the same strain but different stresses

4 different stresses and strains

Manipal UGET-2012

Mechanical Properties of Solids

140897 The pressure applied from all directions on a cube is p. How much its temperature should be raised to maintain the original volume? The volume elasticity of the cube is $β$ and the coefficient of volume expansion is $α$ .

1

\frac{p}{α β}

2

\frac{p α}{β}

3

\frac{p β}{α}

4

\frac{α β}{p}

Explanation:

A If coefficient of volume expansion is $α$ and rise in temperature is $Δ θ$ , then $Δ V = V α Δ θ$
$\frac{Δ V}{V} = α Δ θ$
$∴$ Volume elasticity $(β) = \frac{Stress}{Strain}$
$= \frac{P}{α Δ θ}$
$Δ θ = \frac{p}{α β}$

Mechanical Properties of Solids

140912 The elastic energy stored per unit volume in a stretched wire is

1

\frac{1}{2}

(Young modulus

) (Strain)^{2}

2

\frac{1}{2} (

Stress

) (Strain)^{2}

3

\frac{1}{2} \frac{Stress}{Strain}

4

\frac{1}{2}

(Young modulus) (Stress)

Explanation:

A Energy stored per unit volume.
$E = \frac{1}{2} \times stress \times strain$
We know that,
$Strain = \frac{stress}{Young's modulus (Y)}$
$E = \frac{1}{2} \times Y \times (strain)^{2}$

J and K CET- 2010

Mechanical Properties of Solids

140915 If longitudinal strain for a wire is 0.03 and its Poisson's ratio is 0.5 , then its lateral strain is

1 0.003

2 0.0075

3 0.015

4 0.4

Explanation:

C Poisson 's ratio $= - \frac{lateral strain}{longitudinal strain}$
Longitudinal strain for wire in 0.03 and poisson ratio is 0.5 .
$0.5 = - \frac{lateral strain}{0.03}$
Lateral strain $= - 0.015$
[Negative sign shows decrease in dimension in lateral direction.]

J and K CET- 2006

Mechanical Properties of Solids

140895 A copper wire and a steel wire of the same diameter and length are joined end to end and a force is applied which stretches their combined length by $1 cm$ . Then, the two wires will have

1 the same stress and strain

2 the same stress but different strains

3 the same strain but different stresses

4 different stresses and strains

Manipal UGET-2012

Mechanical Properties of Solids

140897 The pressure applied from all directions on a cube is p. How much its temperature should be raised to maintain the original volume? The volume elasticity of the cube is $β$ and the coefficient of volume expansion is $α$ .

1

\frac{p}{α β}

2

\frac{p α}{β}

3

\frac{p β}{α}

4

\frac{α β}{p}

Explanation:

A If coefficient of volume expansion is $α$ and rise in temperature is $Δ θ$ , then $Δ V = V α Δ θ$
$\frac{Δ V}{V} = α Δ θ$
$∴$ Volume elasticity $(β) = \frac{Stress}{Strain}$
$= \frac{P}{α Δ θ}$
$Δ θ = \frac{p}{α β}$

Mechanical Properties of Solids

140912 The elastic energy stored per unit volume in a stretched wire is

1

\frac{1}{2}

(Young modulus

) (Strain)^{2}

2

\frac{1}{2} (

Stress

) (Strain)^{2}

3

\frac{1}{2} \frac{Stress}{Strain}

4

\frac{1}{2}

(Young modulus) (Stress)

Explanation:

A Energy stored per unit volume.
$E = \frac{1}{2} \times stress \times strain$
We know that,
$Strain = \frac{stress}{Young's modulus (Y)}$
$E = \frac{1}{2} \times Y \times (strain)^{2}$

J and K CET- 2010

Mechanical Properties of Solids

140915 If longitudinal strain for a wire is 0.03 and its Poisson's ratio is 0.5 , then its lateral strain is

1 0.003

2 0.0075

3 0.015

4 0.4

Explanation:

C Poisson 's ratio $= - \frac{lateral strain}{longitudinal strain}$
Longitudinal strain for wire in 0.03 and poisson ratio is 0.5 .
$0.5 = - \frac{lateral strain}{0.03}$
Lateral strain $= - 0.015$
[Negative sign shows decrease in dimension in lateral direction.]

J and K CET- 2006

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