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

The increase in length of a wire on stretching is 0.025%. If its Poisson's ratio is 0.4, then the percentage decrease in diameter is

  1. 0.01%

  2. 0.02%

  3. 0.03%

  4. 0.04%
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Given,

% increase in length of the wire on stretching, $\dfrac{\Delta L}{L}=0.025$%
Poisson's ratio, $v=0.4$
To find: 
% decrease in diameter $= ?$

Poisson's ratio can be given by the formula: 
 $v=-\dfrac{\Delta D/D}{\Delta L/L}$

$\dfrac{\Delta D}{D}=-v\dfrac{\Delta L}{L}$

$\dfrac{\Delta D}{D}=-0.4\times 0.025=-0.01$%
The percentage decreases in diameter is $0.01$%.
The correct option is A.

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

The increase in length of a wire on stretching is 0.025%. If its Poisson's ratio is 0.4, then the percentage decrease in diameter is:

  1. 0.01%

  2. 0.02%

  3. 0.03%

  4. 0.04%
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Increase in length, $\dfrac{\Delta 1}{1}  = 0.025 $%

${\dfrac{\Delta d}{d}} = ?$

Poisson’s ratio is $0.4.$

${Poisson's \ ratio} = \dfrac {\dfrac{\Delta d}{d}} {\dfrac{\Delta l}{l}}\\$

$0.4=\dfrac {\dfrac{\Delta d}{d}} {\dfrac{0.025}{100}}\\$

$\dfrac{\Delta d}{d} = \dfrac{0.4\times 0.025}{100}\\$

$\dfrac{\Delta d}{d} = 0.01$ %

Then the percentage decrease  $= 0.01$ %.

Option A is correct. 

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

For perfectly rigid bodies, the elastic constants Y, B and n are 

  1. Y=B=n =0

  2. Y=B=n =infinity

  3. Y=2B=3n

  4. Y=B=n =0.5
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Perfectly rigid bodies cannot be deformed upon application of any amount of force. Thus, strain is zero or the modulus of elasticity which is inversely proportional to strain becomes infinity

Thus option (b) is the correct option

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

When a uniform metallic wire is stretched the lateral strain produced in it $ \beta.  If \sigma  $ and Y are the pisson 's' ration Young's modulus for wire,then elastic potential energy density of wire is

  1. $ \dfrac {Y\beta^2}{2} $

  2. $ \dfrac {Y\beta^2}{2\sigma^2} $

  3. $ \dfrac {Y \sigma \beta^2}{2} $

  4. $ \dfrac {Y\sigma^2}{2\beta} $
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice physics properties of material substances poisson ratio poisson's ratio elastic energy

A material has poisson's ratio 0.5. If a uniform rod of it suffers a longitudinal strain of $3\times { 10 }^{ -3 }$, what will be percentage increase in volume?

  1. 2%

  2. 3%

  3. 5%

  4. 0%
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Here, $E=3k(1-2\mu)$

where, $E=$Modulus of elasticity
$\mu=$Poisson's ratio
$k=$Modulus of elasticity
Here, $\mu=0.5$ then $k\longrightarrow \infty $
$k=\cfrac { \Delta P }{ \left( \cfrac { \Delta V }{ V }  \right)  } $
If $k\longrightarrow \infty $, then $\Delta V\longrightarrow 0$.
Hence the percentage change in volume$=0\%$

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 } $