Tag: properties of material substances

Questions Related to properties of material substances

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

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

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

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

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

  4. $\displaystyle\frac{\Delta V}{V}=(1-3\mu)\frac{3\Delta l}{l}$

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Correct Option: A
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

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

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

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?

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

  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

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Correct Option: C

Which of the following relation is true?

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

  1. $3Y=K(1+\sigma)$

  2. $K=\displaystyle \frac{9\eta Y}{Y+\eta}$

  3. $\sigma=(6K+\eta)Y$

  4. $\sigma=\displaystyle\frac{0.5Y-\eta}{\eta}$

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Correct Option: D
Explanation:

$Y=2\eta(1+\sigma)\Rightarrow \sigma=\displaystyle\frac{0.5Y-\eta}{\eta}$

Ratio of transverse to axial strain is 

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

  1. Toricelli ratio

  2. Poisson's ratio

  3. Stoke's ratio

  4. Bernoulli's ratio

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Correct Option: B
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.

Possible value of Poisson's ratio is

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

  1. 1

  2. 0.9

  3. 0.8

  4. 0.4

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Correct Option: D
Explanation:

The Poisson's ratio of a stable, isotropic, linear elastic material cannot be less than $1.0$ nor greater than $0.5$. So only possible value among the options is $0.4.$

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. 

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

  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

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Correct Option: C
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.

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

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

  1. Both A & B are true

  2. A is true but B is false

  3. A is true but B is true

  4. Both A & B are false

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Correct Option: D
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. 

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

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

  1. 0.8

  2. 0.35

  3. 0.7

  4. 0.4

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Correct Option: D
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$

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                   

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

  1. 0.00625

  2. 0.125

  3. 0.0125

  4. 0.0625

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Correct Option: C
Explanation:

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

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

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

  1. 0.26

  2. 2.6

  3. 0.026

  4. 0.0026

Show answer
Correct Option: C
Explanation:

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

$\sigma =0.26$ (given)

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

$-0.026=\epsilon y$