Tag: elastic energy

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Questions Related to elastic energy

Multiple choice elastic energy properties of material substances elasticity properties of matter physics

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

  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 } } $
Reveal answer Fill a bubble to check yourself
B Correct answer
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) $ 

Multiple choice elastic energy properties of material substances elasticity properties of matter physics

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:

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

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

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

  4. $2S^2Y$
Reveal answer Fill a bubble to check yourself
C Correct answer
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 $(C)$
Multiple choice elastic energy properties of material substances elasticity properties of matter physics

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 ?

  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. $j _{Cu}= 60 A/cm^2, j _{Al}= 40 A/cm^2$
Reveal answer Fill a bubble to check yourself
C Correct answer
Multiple choice elastic energy properties of material substances elasticity properties of matter physics

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

  1. 1/2

  2. 4

  3. 1/4

  4. 2
Reveal answer Fill a bubble to check yourself
C Correct answer
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)

Multiple choice elastic energy properties of material substances elasticity properties of matter physics

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

  1. 3:1

  2. 2:3

  3. 3:2

  4. 1:3
Reveal answer Fill a bubble to check yourself
D Correct answer
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)

Multiple choice elastic energy properties of material substances elasticity properties of matter physics

The total strain energy stored in a body is known as 

  1. Resilience

  2. Toughness

  3. Modulus of resilience

  4. None of the above
Reveal answer Fill a bubble to check yourself
A Correct answer
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)

Multiple choice elastic energy properties of material substances elasticity properties of matter physics

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

  1. Ductility

  2. Toughness

  3. Resilience

  4. Plasticity
Reveal answer Fill a bubble to check yourself
B Correct answer
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)

Multiple choice elastic energy properties of material substances elasticity properties of matter physics

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

  1. $1.75mm$

  2. $2.0 mm$

  3. $1.50 mm$

  4. $1.25 mm$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Extension deltaL = FL / AY. Since F and A are the same, deltaL is proportional to L/Y. For copper: 1mm = F*1 / (A*1e11). For steel: deltaL_s = F*0.5 / (A*2e11) = 0.25mm. Total extension = 1 + 0.25 = 1.25mm.