Tag: elastic energy

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Questions Related to elastic energy

Multiple choice physics properties of material substances poisson ratio poisson's ratio elastic energy

When a body undergoes a linear tensile strain if experience a lateral contraction also. The ratio of lateral contraction to longitudinal strain is known as

  1. Young's modulus

  2. Bulk modulus

  3. Poisson's law

  4. Hooke's law
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Poisson's ratio is the ratio of transverse contraction strain to longitudinal extension strain in the direction of stretching force

Multiple choice physics properties of material substances poisson ratio poisson's ratio elastic energy

A compressive force is applied to a uniform rod of rectangular cross-section so that its length decreases by $1\%$. If the Poisson’s ratio for the material of the rod be $0.2$, which of the following statements is correct ? The volume approximately .....”

  1. decreases by $1\%$

  2. decreases by $0.8\%$

  3. decreases by $0.6\%$

  4. increases by $0.2\%$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$V=Al=abl; \dfrac{\triangle a}{a}=\dfrac{\triangle b}{b}\left[\because \sigma=\dfrac{\dfrac{-\triangle a}{a}}{\dfrac{\triangle l}{l}}=\dfrac{\dfrac{\triangle b}{b}}{\dfrac{\triangle l}{l}}\right]$
$\Rightarrow \dfrac{\triangle V}{V}=2\dfrac{\triangle a}{a}+\dfrac{\triangle I}{l}=-2\sigma \dfrac{\triangle I}{I}+\dfrac{\triangle I}{I}\Rightarrow \dfrac{\triangle V}{V}=\dfrac{\triangle I}{I}(1-2\sigma)-1(1-2\times 0.2)=-1(1-0.4)=-0.6$
$\because$ The volume approximately decreases by $0.6\%$.

Multiple choice physics properties of material substances poisson ratio poisson's ratio elastic energy

When a rubber cord is stretched, the change in volume is negligible compared to the change in its linear dimension. Then poisson's ratio for rubber is

  1. infinite

  2. zero

  3. 0.5

  4. -1
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

By Lame's relation, $\ \nu = \dfrac { 1 }{ 2 } -\dfrac { E  }{ 6B} ,$ where  $B$ is bulk modulus.
Given, volume change is negligible, thus B tends to infinity. $(B=-V\dfrac { dP }{ dV } )$
 Thus, $\nu=\dfrac { 1 }{ 2 } $

Multiple choice physics properties of material substances poisson ratio poisson's ratio elastic energy

The Poisson's ratio $\sigma$ should satisfy the relation :

  1. -1< $\sigma $ < 0.5

  2. -0.5 < $\sigma $ < 1.0

  3. 0.5 < $\sigma $ < 1.0

  4. -1.0 < $\sigma $ < -0.5
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Poisson's ratio is the ratio of transverse contradiction strain to longitudinal extension strain in the direction of stretching force.

The Poisson's ratio $\sigma$ should satisfy the relation,
$-1<\sigma <0.5$

Multiple choice physics properties of material substances poisson ratio poisson's ratio elastic energy

A metallic wire of young's modulus Y and poisson's ratio $\sigma$, length L and area of cross section A is stretched by a load of W kg. The increase in volume of the wire is:

  1. $\sigma (W^2 L/2AY^2)$

  2. $\sigma (W^2 L/AY^2)$

  3. $\sigma (W^2 L/4AY^2)$

  4. $\sigma (2W^2 L/AY^2)$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

We know that $\sigma =(\Delta A/A) / (\Delta L/L)=(\Delta V/V)/(\Delta L/L)^2 \implies \Delta V=\sigma (\Delta L/L)^2V$

We also know $Y=(W/A)/(\Delta L/L) \implies (\Delta L/L)=W/AY$

Substituting this value in the previous expression, we get, $\Delta V=\sigma (W/AY)^2V=\sigma (W^2 L/AY^2)$

The correct option is (b)

Multiple choice physics properties of material substances poisson ratio poisson's ratio elastic energy

Poisson' ratio is defined as the ratio of 

  1. longitudinal stress and longitudinal strain

  2. longitudinal stress and lateral stress

  3. lateral stress and longitudinal stress

  4. lateral stress and lateral strain
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Poisson' ratio is defined as the ratio of lateral stress and longitudinal stress

The correct option is (c)

Multiple choice physics properties of material substances poisson ratio poisson's ratio elastic energy

A metal wire of length L is loaded and an elongation of $\Delta L$ is produced. If the area of cross section of the wire is A, then the change in volume of the wire, when elongated is . Take Poisson's ratio as 0.25

  1. $\Delta V=(\Delta L)^2A/L$

  2. $\Delta V=(\Delta L)^2A/4L$

  3. $\Delta V=(\Delta L)^2A/2L$

  4. $\Delta V=(\Delta L)^2A/3L$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

We know that $\sigma =(\Delta A/A) / (\Delta L/L)=(\Delta V/V)/(\Delta L/L)^2 \implies \Delta V=\sigma (\Delta L/L)^2V=\sigma (\Delta L/L)^2(LA)=\sigma (\Delta L)^2A/L$

Substituting $\sigma=0.25$, we get, $\Delta V=(\Delta L)^2A/4L$

The correct option is (b)

Multiple choice physics properties of material substances poisson ratio poisson's ratio elastic energy

The change in unit volume of a material under tension with increase in its poisson's ratio will be

  1. Increase

  2. Decrease

  3. Remains same

  4. Initially increases and then decreases
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The poisson's ratio is related to modulus of elasticity as $Y = 3B(1-2 \sigma)$. Since stress is same for Y and B, we get, $dL/L=dV/3V(1-2 \sigma) \implies dV=3V (dL/L)(1-2 \sigma)$
As $\sigma$ is increased, $dV$ decreases. 

The correct option is (b)