Tag: poisson's ratio

Questions Related to 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}} $

A cylinderical wire of radius $1 mm,$ length $1 m,$ Young's modulus = $2\times10^{11}N/m^2$, poisson's ratio $\mu =\pi/10$ is stretched by a force of $100N$. Its radius will become

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

  1. $0.99998 mm$

  2. $0.99999 mm$

  3. $0.99997 mm$

  4. $0.99995 mm$

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Correct Option: C

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?

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

  1. $2\%$

  2. $3\%$

  3. $5\%$

  4. $0\%$

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Correct Option: D

The poisson's ratio can not be

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

  1. $-1$

  2. $0$

  3. $0.25$

  4. $0.5$

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Correct Option: C

A cube of wood supporting $200 gm$ mass just in water $(\rho =1g/cc)$. When the mass is removed, the cube rises by $2cm$. The volume of cube is

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

  1. $1000 cc$

  2. $800cc$

  3. $500 cc$

  4. None of these

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Correct Option: D
Explanation:
Let the edge of cube be $L$ when mass is on the cube of wood 
$200g+{ L }^{ 3 }{ d } _{ wood }g={ L }^{ 3 }{ d } _{ water }g$
$\Rightarrow { L }^{ 3 }{ d } _{ wood }g={ L }^{ 3 }{ d } _{ water }g$
$\Rightarrow { L }^{ 3 }{ d } _{ wood }g={ L }^{ 3 }{ d } _{ water }g-200g$
$\Rightarrow { L }^{ 3 }{ d } _{ wood }={ L }^{ 3 }d-200$
When mass is removed
${ L }^{ 3 }{ d } _{ wood }-\left( L-2 \right) { L }^{ 2 }{ d } _{ water }\quad \longrightarrow \left( 2 \right) $
From $(1)$ and $(2)$
${ L }^{ 3 }{ d } _{ water }-200=\left( L-2 \right) { L }^{ 2 }{ d } _{ water }$
But ${ d } _{ water }=1$
$\therefore$    ${ L }^{ 3 }-200={ L }^{ 2 }\left( L-2 \right) $
$\therefore$    $L=10cm$.

what is the ratio of Youngs modulus $E$ to shear modulus $G$ in terms of poissons ratio$?$

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

  1. $2\left( {1 + \mu } \right)$

  2. $2\left( {1 - \mu } \right)$

  3. $\frac{1}{2}\left( {1 - \mu } \right)$

  4. $\frac{1}{2}\left( {1 + \mu } \right)$

Show answer
Correct Option: A
Explanation:

As we know$:-$

$G = \frac{E}{{2\left( {1 + \mu } \right)}}$ 
so this gives the ratio of $E$ to $G = 2\left( {1 + \mu } \right)$
Hence,
option $(A)$ is correct answer.

For a given material, the Young's modulus is 2.4 times its modulus of rigidity. Its Poisson's ratio is

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

  1. $0.2$

  2. $0.4$

  3. $1.2$

  4. $2.4$

Show answer
Correct Option: A
Explanation:

$Y = 2\eta \left( {1 + \sigma } \right)$

But $Y = 2.4\eta $
$\therefore 2.4\eta  = 2\eta \left( {1 + \sigma } \right)$
$\left( {1 + \sigma } \right) = 1.2$
$\sigma  = 0.2$
Hence,
option $(A)$ is correct answer.

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: C

If rigidity modulus is 2.6 times of youngs modulus then the value of poission's ratio is 

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

  1. 0.2

  2. 0.3

  3. 0.5

  4. 0.1

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Correct Option: B