Tag: elastic energy

Questions Related to elastic energy

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

elastic energy properties of material substances elasticity properties of matter physics

  1. $\cfrac { 1 }{ 2 } \cfrac { { \left( stress \right) }^{ } }{ Y } $

  2. $\cfrac { 1 }{ 2 } \cfrac { { \left( stress \right) }^{ 2 } }{ Y } $

  3. $\cfrac { 1 }{ 2 } \cfrac { { \left( stress \right) }^{ 2 } }{ { Y }^{ 2 } } $

  4. $\cfrac { 1 }{ 2 } \cfrac { { \left( stress \right) }^{ } }{ { Y }^{ 2 } } $

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Correct Option: B
Explanation:

The elastic energy stored per unit volume in a stretched wire is
$u=\cfrac { 1 }{ 2 } \times stress\times strain=\dfrac { { (stress) }^{ 2 } }{ 2Y } \left( \because Y=\cfrac { stress }{ strain }  \right) $ 

If S is stress and Y is Young's modulus of the material of a wire, the energy stored in the wire per unit volume is:

elastic energy properties of material substances elasticity properties of matter physics

  1. $\frac{S}{2Y}$

  2. $\frac{2Y}{S^2}$

  3. $\frac{S^2}{2Y}$

  4. $2S^2Y$

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Correct Option: C
Explanation:
Energy stored per unit volume can be given as: 
 $E  =\dfrac{1}{2} \times stress \times strain $ -----------(1)      
From Hooke's law :
Young's modulus, $Y = \dfrac{Stress}{Strain}$

$\implies$    $Strain   = \dfrac{Stress}{Y}   = \dfrac{S}{Y}$ -----------(2)  
  
From equation (1) and (2): 
$\therefore$    $E = \dfrac{1}{2} \times S \times \dfrac{S}{Y} $

$\Rightarrow E=  \dfrac{1}{2} \dfrac{S^2}{Y}$
Hence, the correct option is $(C)$

One end of an aluminium wire whose diameter is 2.5 mm is welded to one end of a copper diameter is 1.8 mm. The composite wire carries a steady current i of I .3 A. What is the current density in each wire ?

elastic energy properties of material substances elasticity properties of matter physics

  1. $j _{Cu}= 26 A/cm^2, j _{Al}= 51 A/cm^2$

  2. $j _{Cu}=51A/cm^2 , j _{Al}= 26A/cm^2$

  3. $j _{Cu}=40A/cm^2, j _{Al}= 60 A/cm^2$

  4. $j _{Cu}= 60 A/cm^2, j _{Al}= 40 A/cm^2$

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Correct Option: C

Two wires are of same material. Wire 1 is of 4 times longer than wire 2 and area of wire 1 is 4 times less than wire 2. Compare the stresses if they are elongated by the same load

elastic energy properties of material substances elasticity properties of matter physics

  1. 1/2

  2. 4

  3. 1/4

  4. 2

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Correct Option: C
Explanation:

The stress is given by Force/Area . 
Comparing the stresses, we get, $(stress _1/stress _2)=(L _2/L _1)=1/4$

The correct option is (c)

Two wires of different material but of same radius and length are stretched by the same load, the ratio of the stresses in the material will be same

elastic energy properties of material substances elasticity properties of matter physics

  1. True

  2. False

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Correct Option: A
Explanation:

The stress depends only on the load and the area of cross section. Thus, the stress produces will also be same

Two wires of different material but of same radius and different length are stretched by the loads in the ratio 1:3, the ratio of the stresses in the material will be same

elastic energy properties of material substances elasticity properties of matter physics

  1. 3:1

  2. 2:3

  3. 3:2

  4. 1:3

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Correct Option: D
Explanation:

The stress is directly proportional to the force applied and the inversely proportional to area of cross section. Thus as force ratio is 1:3, the stress ratio will also be 1:3

The correct option is (d)

The total strain energy stored in a body is known as 

elastic energy properties of material substances elasticity properties of matter physics

  1. Resilience

  2. Toughness

  3. Modulus of resilience

  4. None of the above

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Correct Option: A
Explanation:

The strain energy is released when the object is unloaded, which is nothing but resilience

Resilience is the ability of a material to absorb energy when deformed, and release that energy upon unloading

The correct option is (a)

A material capable of absorbing large amount of energy before fracture is known as 

elastic energy properties of material substances elasticity properties of matter physics

  1. Ductility

  2. Toughness

  3. Resilience

  4. Plasticity

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Correct Option: B
Explanation:

Toughness is the ability of a material to absorb energy and plastically deform without fracturing. 

It is defined as the amount of energy per unit volume that a material can absorb before rupturing.

The correct option is option(b)

A copper wire $1.0$ m and a steel wire of length $0.5$ m having equal cross-sectional areas are joining end to end. The composite wire is stretched by a certain load which stretches the copper wire by $1$ mm. If the Young's modulus  of copper steel are respectively $1.0\times 11^{11}Nm^{-1}$ and $ 2.0 \times 10^{11} Nm^{-2}$, the total extension of the composite wire is

elastic energy properties of material substances elasticity properties of matter physics

  1. $1.75mm$

  2. $2.0 mm$

  3. $1.50 mm$

  4. $1.25 mm$

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Correct Option: D

Give the MKS units for the following quantities.
Young's modulus.

elastic energy properties of material substances elasticity properties of matter physics

  1. $2N/m^2$.

  2. $3N/m^2$.

  3. $4N/m^2$.

  4. $N/m^2$.

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Correct Option: D