Tag: properties of material substances

Questions Related to properties of material substances

If Young modulus is three times of modulus of rigidity, then Poisson ratio is equal to:

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

  1. $0.2$

  2. $0.3$

  3. $0.4$

  4. $0.5$

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Correct Option: D
Explanation:

Given,


$E=3G$

$2(1+m)=\dfrac{3G}{G}$

$m=\dfrac{3}{2}-1=\dfrac{1}{2}=0.5$

A material has Poissons ratio $0.5$. If a uniform rod made of the surface a longitudinal string of $2\times {10}^{-3}$, what is the percentage increase in its volume?

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

  1. $2\%$

  2. $4\%$

  3. $0\%$

  4. $5\%$

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Correct Option: B

A steel wire of length $30cm$ is stretched ti increase its length by $0.2cm$. Find the lateral strain in the wire if the poisson's ratio for steel is $0.19$ :

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

  1. $0.0019$

  2. $0.0008$

  3. $0.019$

  4. $0.008$

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Correct Option: A
Explanation:

Poisson's ratio $=-\cfrac{\epsilon _{lateral}}{\epsilon _{Longtudinal}}$

$\epsilon _{longitudinal}=\cfrac{\triangle L}{L}=\cfrac{0.2}{20}$
$\therefore \epsilon _{lateral}=-\cfrac{0.2}{20}\times 0.19$
$=-0.0019$
$|\epsilon _{lateral}|=0.0019$

For a material $Y={ 6.6\times 10 }^{ 10 }\ { N/m }^{ 2 }$ and bulk modulus $K{ 11\times 10 }^{ 10 }\ { N/m }^{ 2 }$, then its Poisson's ratio is:

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

  1. $0.8$

  2. $0.35$

  3. $0.7$

  4. $0.4$

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Correct Option: D
Explanation:

Given that,

Young’s modulus $Y=6.6\times {{10}^{10}}\,N/{{m}^{2}}$

Bulk modulus $B=11\times {{10}^{10}}\,N/{{m}^{2}}$

We know that,

  $ Y=3K\left( 1-2\mu  \right) $

 $ 6.6\times {{10}^{10}}=3\times 11\times {{10}^{10}}-66\times {{10}^{10}}\mu  $

 $ -\mu =\dfrac{\left( 6.6-33 \right)\times {{10}^{10}}}{66\times {{10}^{10}}} $

 $ \mu =0.4 $

Hence, the poisson’s ratio is $0.4$

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

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

  1. $0.01$

  2. $0.02$

  3. $0.03$

  4. $0.04$

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Correct Option: A
Explanation:

Suppose, D be the diameter of the wire Poissons ratio,  

$σ=\frac { lateral strain }{ longitudinal strain } $

 $σ=\frac { \frac { ΔD }{ D }  }{ \frac { ΔL }{ L }  } $

 $\frac { ΔL }{ L } =0.025$

 $σ=0.004$

 $σ=\frac { \frac { ΔD }{ D }  }{ \frac { 1 }{ 40 }  } $

 $\frac { ΔD }{ D } =\frac { 1 }{ 40 } \times 0.4=0.01$

When a wire is stretched, its length increases by 0.3% and the diameter decreases by 0.1%. Poisson's ratio of the material of the wire is about

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

  1. 0.03

  2. 0.333

  3. 0.15

  4. 0.015

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Correct Option: A

A material has Poisson's ratio 0.5. If a uniform rod of it suffers a longitudinal strain of $2\times { 10 }^{ -3 }$, then the percentage increase in its volume is 

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

  1. 0%

  2. 10%

  3. 20%

  4. 5%

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Correct Option: A

When a metal wire is stretched by a load, the fractional change in its volume $\Delta V/V$ is proportional to?

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

  1. $-\dfrac{\Delta l}{l}$

  2. $\left(\dfrac{\Delta l}{l}\right)^2$

  3. $\sqrt{\Delta l/l}$

  4. None of these

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Correct Option: A
Explanation:

$v=\dfrac { \pi { d }^{ 2 }l }{ 4 } $ 


$⟹\dfrac { ΔV }{ V } =\dfrac { 2Δd }{ d } +\dfrac { Δl }{ l } $

 $⟹d\frac { ΔV }{ V } =\dfrac { (1−2σ)Δl }{ l } $

$(\dfrac { Δd }{ d } =\dfrac { −σΔl }{ l } )$

where $σ$ is Poisson's ratio.

A material has poisson's ratio $0.3$. If a uniform rod of it suffers a longitudinal strain of $25\times 10^{-3}$, then the percentage increase in its volume is

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

  1. $1\%$

  2. $2\%$

  3. $3\%$

  4. $4\%$

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Correct Option: C

The Young's modulus of the material of a wire is $6\times 10^{12}$$N/m^{2}$ and there is no transverse in it, then its modulus of rigidity will be 

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

  1. $3\times 10^{12}N/m^{2}$

  2. $2\times 10^{12}N/m^{2}$

  3. $ 10^{12}N/m^{2}$

  4. None of the above

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Correct Option: A
Explanation:

Relation between young’s modulus and transverse strain is as follows:

$Y=2\eta \left( 1+\sigma  \right)$

Where, \[$\eta ]$is modulus of rigidity

And $\sigma $is transverse strain, $\sigma =0$

So,

$ Y=2\eta  $

$ \eta =\dfrac{Y}{2}=\dfrac{6\times {{10}^{12}}}{2}=3\times {{10}^{12}}\,N/{{m}^{2}} $