Tag: poisson ratio

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Questions Related to poisson ratio

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

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 

  1. 1

  2. 0.25

  3. 0.5

  4. 0.75
Reveal answer Fill a bubble to check yourself
C Correct answer
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.

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

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

  1. $0.5$
  2. $0.4$
  3. $0.2$
  4. $0.3$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The relation between Young's modulus Y, rigidity modulus eta, and Poisson's ratio sigma is Y = 2 * eta * (1 + sigma). Given Y = 2.4 * eta, we substitute to get 2.4 * eta = 2 * eta * (1 + sigma), which simplifies to 1.2 = 1 + sigma, giving sigma = 0.2.

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

Which of the following pairs is not correct?

  1. strain-dimensionless
  2. stress-$N/m^{2}$
  3. modulus of elasticity-$N/m^{2}$
  4. poisson's ratio-$N/m^{2}$
Reveal answer Fill a bubble to check yourself
D Correct answer
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

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

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

  1. $Y=2\eta(1+\sigma)$
  2. $\eta=2Y(1+\sigma)$
  3. $\displaystyle \sigma=\frac{2Y}{(1+\eta)}$
  4. $Y=\eta(1+\sigma)$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

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

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

Poisson's ratio cannot exceed

  1. 0.25

  2. 1.0

  3. 0.75

  4. 0.5
Reveal answer Fill a bubble to check yourself
D Correct answer
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 $\mu=0.5$

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

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 :

  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. $\dfrac { l M } { \pi l \rho R ^ { 3 } }$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Poisson's ratio = - (dr/r) / (dl/l). Using the volume of the wire V = pi * R^2 * l, and assuming constant volume or relating the changes, the expression for Poisson's ratio is derived as (r * M) / (pi * l * rho * R^3).

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 ratio is 0.4, then the percentage decrease in the 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

Poisson's ratio is sigma = (percentage decrease in diameter) / (percentage increase in length). Given sigma = 0.4 and longitudinal increase = 0.025%, the percentage decrease in diameter is 0.4 * 0.025% = 0.01%.