Tag: elastic energy

Questions Related to elastic energy

The poisson's ratio can not be

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

  1. $-1$

  2. $0$

  3. $0.25$

  4. $0.5$

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Correct Option: C

A cube of wood supporting $200 gm$ mass just in water $(\rho =1g/cc)$. When the mass is removed, the cube rises by $2cm$. The volume of cube is

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

  1. $1000 cc$

  2. $800cc$

  3. $500 cc$

  4. None of these

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Correct Option: D
Explanation:
Let the edge of cube be $L$ when mass is on the cube of wood 
$200g+{ L }^{ 3 }{ d } _{ wood }g={ L }^{ 3 }{ d } _{ water }g$
$\Rightarrow { L }^{ 3 }{ d } _{ wood }g={ L }^{ 3 }{ d } _{ water }g$
$\Rightarrow { L }^{ 3 }{ d } _{ wood }g={ L }^{ 3 }{ d } _{ water }g-200g$
$\Rightarrow { L }^{ 3 }{ d } _{ wood }={ L }^{ 3 }d-200$
When mass is removed
${ L }^{ 3 }{ d } _{ wood }-\left( L-2 \right) { L }^{ 2 }{ d } _{ water }\quad \longrightarrow \left( 2 \right) $
From $(1)$ and $(2)$
${ L }^{ 3 }{ d } _{ water }-200=\left( L-2 \right) { L }^{ 2 }{ d } _{ water }$
But ${ d } _{ water }=1$
$\therefore$    ${ L }^{ 3 }-200={ L }^{ 2 }\left( L-2 \right) $
$\therefore$    $L=10cm$.

what is the ratio of Youngs modulus $E$ to shear modulus $G$ in terms of poissons ratio$?$

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

  1. $2\left( {1 + \mu } \right)$

  2. $2\left( {1 - \mu } \right)$

  3. $\frac{1}{2}\left( {1 - \mu } \right)$

  4. $\frac{1}{2}\left( {1 + \mu } \right)$

Show answer
Correct Option: A
Explanation:

As we know$:-$

$G = \frac{E}{{2\left( {1 + \mu } \right)}}$ 
so this gives the ratio of $E$ to $G = 2\left( {1 + \mu } \right)$
Hence,
option $(A)$ is correct answer.

For a given material, the Young's modulus is 2.4 times its modulus of rigidity. Its Poisson's ratio is

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

  1. $0.2$

  2. $0.4$

  3. $1.2$

  4. $2.4$

Show answer
Correct Option: A
Explanation:

$Y = 2\eta \left( {1 + \sigma } \right)$

But $Y = 2.4\eta $
$\therefore 2.4\eta  = 2\eta \left( {1 + \sigma } \right)$
$\left( {1 + \sigma } \right) = 1.2$
$\sigma  = 0.2$
Hence,
option $(A)$ is correct answer.

When a wire is stretched, its length increases by $0.3$% and the diameter decreases by $0.1$%. Poisson's ratio of the material of the wire is about   

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

  1. $0.03$

  2. $0.333$

  3. $0.15$

  4. $0.015$

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Correct Option: C

If rigidity modulus is 2.6 times of youngs modulus then the value of poission's ratio is 

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

  1. 0.2

  2. 0.3

  3. 0.5

  4. 0.1

Show answer
Correct Option: B

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 

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

  1. 1

  2. 0.25

  3. 0.5

  4. 0.75

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Correct Option: C
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.

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

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

  1. $0.5$

  2. $0.4$

  3. $0.2$

  4. $0.3$

Show answer
Correct Option: A

The ratio of change in dimension at right angles to applied force to the initial dimension is defined as

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

  1. $Y$

  2. $\eta$

  3. $\beta$

  4. $K$

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Correct Option: C
Explanation:

This is a factual question. The ratio is labelled $\beta$.

Which of the following pairs is not correct?

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

  1. strain-dimensionless

  2. stress-$N/m^{2}$

  3. modulus of elasticity-$N/m^{2}$

  4. poisson's ratio-$N/m^{2}$

Show answer
Correct Option: D
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