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

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.

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

Consider the statements A and B, identify the correct answer given below :
(A) : If the volume of a body remains unchanged when subjected to tensile strain, the value of poisson's ratio is 1/2.
(B) : Phosper bronze has low Young's modulus and high rigidity modulus. 

  1. A and B are correct

  2. A and B are wrong

  3. A is correct and B is wrong

  4. A is wrong and B is right
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Experimental value of poisson's ratio is always between $0$ to $1/2$ .

As Phosper bronze is solid so, value of young's modulus is also high.

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

Consider the following two statements A and B and identify the correct answer.
A) When the length of a wire is doubled, the Young's modulus of the wire is also doubled
B) For elastic bodies Poisson's ratio is + Ve and for inelastic bodies Poissons ratio is -Ve

  1. Both A &amp; B are true

  2. A is true but B is false

  3. A is true but B is true

  4. Both A &amp; B are false
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

1/ Young's modulis is property of a metal independent of its dimensions
2/Definition of Poisson's ratio 
Poisson's ratio is the ratio of transverse contraction strain to longitudinal extension strain in the direction of stretching force. Tensile deformation is considered positive and compressive deformation is considered negative. The definition of Poisson's ratio contains a minus sign so that normal materials have a positive ratio.Virtually all common materials, such as the blue rubber band on the right, become narrower in cross section when they are stretched. 

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

For a material Y $=$ 6.6x10$^{10}$ N/m$^{2}$ and bulk modulus K $=$ 11x10$^{10}$ N/m$^{2}$, then its Poissons's ratio is

  1. 0.8

  2. 0.35

  3. 0.7

  4. 0.4
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Relation  between  Young's  modulus,  bulk  modulus  and  poisson's  ratio  is  given  below :
$Y = 3B (1-2\sigma)$
So,  according  to  problem
$ 6.6 \times  10^{10} = 3 \times 11 \times 10^{10} (1-2\sigma)$
$ \sigma = 0.4$

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

A wire is subjected to a longitudinal strain of $0.05.$ If its material has a Poisson's ratio $0.25$, the lateral strain experienced by it is                   

  1. 0.00625

  2. 0.125

  3. 0.0125

  4. 0.0625
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$\epsilon x=0.05$  (given)
$\sigma =0.25$
$\dfrac{\epsilon y}{0.05}=-0.25$ (standard result)
$=-0.0125$

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

A $3 cm$ long copper wire is stretched to increase its length by $0.3cm.$ If poisson's ratio for copper is $0.26$, the lateral strain in the wire is

  1. 0.26

  2. 2.6

  3. 0.026

  4. 0.0026
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$\epsilon x=\dfrac{0.3}{3}$$=0.1$ (standard result)

$\sigma =0.26$ (given)

$0.26=\dfrac{-\epsilon y}{0.1}$

$-0.026=\epsilon y$