Tag: poisson's ratio

Questions Related to poisson's ratio

When a rubber cord is stretched, the change in volume with respect to change in its linear dimensions is negligible. The Poisson's ratio for rubber is 

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

  1. 1

  2. 0.25

  3. 0.5

  4. 0.75

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Correct Option: C
Explanation:

$V = \pi {r^2}I$

$\frac{{\Delta V}}{V} = \frac{{\Delta \left( {\pi {r^2}I} \right)}}{{\pi {r^2}I}}$
$\frac{{\Delta V}}{V} = \frac{{{r^2}\Delta I + 2rI\Delta r}}{{{r^2}I}}$
$\frac{{\Delta V}}{V} = \frac{{\Delta I}}{I} + \frac{{2\Delta r}}{r}$
But $\frac{{\Delta V}}{V} = 0$
therefore$,$ $\frac{{\Delta I}}{I} = \frac{{ - 2\Delta r}}{r}$
Now$,$ Poisson's ratio$,$ $\sigma  = \frac{{\frac{{ - \Delta r}}{r}}}{{\frac{{\Delta I}}{I}}}$-------------------$(1)$
from equation $(1),$
$\sigma  =  - \left( {\frac{{\frac{{\Delta r}}{r}}}{{\frac{{ - 2\Delta r}}{r}}}} \right) = \frac{1}{2} = 0.5$
Hence,
option $(C)$ is correct answer.

For a given material, the Youngs modulas is $2.4$ times its modulus of rigidity. What is the value of its poissons ratio ?

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

  1. $0.5$

  2. $0.4$

  3. $0.2$

  4. $0.3$

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Correct Option: A

The ratio of change in dimension at right angles to applied force to the initial dimension is defined as

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

  1. $Y$

  2. $\eta$

  3. $\beta$

  4. $K$

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Correct Option: C
Explanation:

This is a factual question. The ratio is labelled $\beta$.

Which of the following pairs is not correct?

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

  1. strain-dimensionless

  2. stress-$N/m^{2}$

  3. modulus of elasticity-$N/m^{2}$

  4. poisson's ratio-$N/m^{2}$

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Correct Option: D
Explanation:

stress is $\dfrac{F}{A}$ hence unit $N/m^2$

strain is $\dfrac{\Delta l}{L}$ so unit $m/m$ therefore dimensionless
modulus of elasticity is $ \dfrac{stress}{strain}$ hence same unit  as stress as the denominator is dimensionless
poisson's ratio $\dfrac{-\epsilon _t}{\epsilon _l} $ so its also going to be dimensionless

For which value of Poisson's ratio the volume of a wire does not change when it is subjected to a tension?

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

  1. 0.5

  2. -1

  3. 0.1

  4. 0

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Correct Option: A

The relationship between Y, $\eta$ and $\sigma$ is

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

  1. $Y=2\eta(1+\sigma)$

  2. $\eta=2Y(1+\sigma)$

  3. $\displaystyle \sigma=\frac{2Y}{(1+\eta)}$

  4. $Y=\eta(1+\sigma)$

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Correct Option: A
Explanation:

By using stress relations on unit solid element, this relation can be derived:
$\eta \quad =\quad \dfrac { Y }{ 2(1+\sigma ) } \ Thus,\quad Y=2\eta (1+\sigma )$

Poisson's ratio can not have the value:

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

  1. 0.1

  2. 0.7

  3. 0.2

  4. 0.5

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Correct Option: C

Poisson's ratio cannot exceed

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

  1. 0.25

  2. 1.0

  3. 0.75

  4. 0.5

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Correct Option: D
Explanation:

Poisson's ratio = Lateral strain/Longitudinal strain

$Y=3K(1-2\mu)\Rightarrow \mu=0.5-Y/6K$
$Y$ is young's modulus.
$\mu$ is poisson ratio
$K$ is compressibility of the substance which is inverse of Bulk's modulus. Maximum value of $K$ is $\infty$
So maximum value of Poisson's ratio $\mu=0.5$

A wire of mass $M ,$ density $\rho$ and radius $R$ is stretched. If $r$ is the change in the radius and $l$ is the change in its length, then Poisson's ratio is given by :

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

  1. $\dfrac { \pi l } { \rho M r R ^ { 3 } }$

  2. $\dfrac { R M \pi } { l \rho r ^ { 3 } }$

  3. $\dfrac { r M } { \pi l \rho R ^ { 3 } }$

  4. $\dfrac { l M } { \pi l \rho R ^ { 3 } }$

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Correct Option: C

The increase in length of a wire on stretching is 0.025% If its poisson 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: C