Tag: poisson ratio

Questions Related to poisson ratio

The formula $Y=3B(1-2 \sigma)$ relates young's modulus and bulk's modulus with poisson's ratio. A theoretical physicist derives this formula incorrectly as $Y=3B(1-4 \sigma)$. According to this formula, what would be the theoretical limits of poisson's ratio:

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

  1. Poisson's ratio should be less than 1

  2. Poisson's ratio should be less than 0.5

  3. Poisson's ratio should be less than 0.25

  4. Poisson's ratio should be less than 0

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Correct Option: C
Explanation:

In the formula derived by the student, in order that Y is positive, $\sigma<0.25$, else Y will be negative, which is not possible

Hence, poisson's ratio should be less than 0.25

The correct option is option(c)

The ice storm in the state of Jammu strained many wires to the breaking point. In a particular situation, the transmission towers are separated by $500\ m$ of wire. The top grounding wire $15^{o}$ from horizontal at the towers, and has a diameter of $1.5cm$. The steel wire has a density of $7860\ kg\ m^{-3}$. When ice (density $900\ kg\ m^{-3}$) built upon the wire to a diameter $10.0\ cm$, the wire snapped. What was the breaking stress (force/ unit area) in $N\ m^{-2}$ in the wire at the breaking point? You may assume the ice has no strength.

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

  1. $7.4\ \times 10^{7}\ N\ m^{-2}$

  2. $4.5\ \times 10^{8}\ N\ m^{-2}$

  3. $2.6\ \times 10^{6}\ N\ m^{-2}$

  4. $1.15\ \times 10^{7}\ N\ m^{-2}$

Show answer
Correct Option: C

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. $0.5$

Show answer
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. $0.008$

Show answer
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. $0.4$

Show answer
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. $0.04$

Show answer
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

Show answer
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.