Tag: properties of material substances

Quizzes (4) Questions (125)

Questions Related to properties of material substances

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

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).