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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

A uniform bar of length 'L' and cross sectional area 'A' is subjected to a tensile load 'F'. 'Y' be the Young modulus and '$\sigma$' be the Poisson's ratio then volumetric strain is  

  1. $\frac{F}{AY}(1 - \sigma)$

  2. $\frac{F}{AY}(2 - \sigma)$

  3. $\frac{F}{AY}(1 - 2\sigma)$

  4. $\frac{F}{AY} \sigma$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Volumetric strain is defined as the change in volume divided by the original volume. For a bar under uniaxial stress, the longitudinal strain is F/(AY) and the lateral strains are -sigma * F/(AY). Summing these gives the volumetric strain: F/(AY) * (1 - 2*sigma).

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

A copper rod of length $l$ is suspended from the ceiling by one of its ends. Find the relative increment of its volume $\displaystyle\frac{\Delta V}{V}$.

  1. $\displaystyle\frac{\Delta V}{V}=(1-2\mu)\frac{\Delta l}{l}$

  2. <span>$\displaystyle\frac{\Delta V}{V}=(1-3\mu)\frac{\Delta l}{l}$</span>

  3. <span>$\displaystyle\frac{\Delta V}{V}=(1-2\mu)\frac{2\Delta l}{l}$</span>

  4. <span>$\displaystyle\frac{\Delta V}{V}=(1-3\mu)\frac{3\Delta l}{l}$</span>
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

We can take copper rod as cylindrical rod

$v=\pi r^2 l$

$E=\dfrac{\Delta l}{l}$ (longitudinal strain)

$E'=\dfrac{\Delta r}{r}=-\mu E$  ,where $\mu$ is Poisson ratio,$E'$ is lateral strain

$\dfrac{\Delta V}{V}=\dfrac{2\Delta r}{r}+\dfrac{\Delta l}{l}$

$\dfrac{\Delta V}{V}=(1-2\mu)\dfrac{\Delta l}{l}$

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

One end of a wire $2$ m long and diameter $2$ mm, is fixed in a ceiling. A naughty boy of mass $10$ kg jumps to catch the free end and stays there. The change in length of wire is (Take $g=10m/s^2, Y=2\times 10^{11} N/m^2$).
In above problem, if Poisson's ratio is $\sigma =0.1$, the change in diameter is?

  1. $3.184\times 10^{-5}$ m

  2. $31.84\times 10^{-5}$ m

  3. $3.184\times 10^{-8}$ m

  4. $31.84\times 10^{-8}$ m
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

First, calculate longitudinal strain: delta_L/L = F/(AY) = (mg)/(pi * r^2 * Y). Then, use Poisson's ratio sigma = -(delta_d/d) / (delta_L/L) to find the change in diameter. Plugging in the values yields 3.184 * 10^-8 m.

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

Ratio of transverse to axial strain is 

  1. Toricelli ratio

  2. Poisson's ratio

  3. Stoke's ratio

  4. Bernoulli's ratio
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Hookes law states that stress is proportional to strain up to elastic limit. If p is the stress induced in material and e the corresponding strain, then according to Hooke's law, 
$\dfrac{P}{E}$ = E, a constant.