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

The theoretical limits of poisson's ratio lies between -1 to 0.5 because

  1. Shear modulus and bulk's modulus should be positive

  2. Bulk's modulus is negative during compression

  3. Shear modulus is negative during compression

  4. Young's modulus should be always positive
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let Y, K, n and $\sigma$ be the Young's Modulus, Bulk modulus, Modulus of Rigidity and Poisson's Ratio, respectively. 
Y = 3K (1 - 2$\sigma$) [Standard formula] 
Y = 2n (1 + $\sigma$) [Standard formula] 
Hence, 3K (1 - 2$\sigma$) = 2n (1 + $\sigma$) 
Now K and n are always positive, so 
i) If $\sigma$ be +ve, then RHS is always +ve. So LHS must also be +ve. Therefore, 2$\sigma$ < 1 or $\sigma$ <1/2 
ii) If $\sigma$ be -ve, then LHS will always be +ve. Therefore, 1+$\sigma$ > 0 or $\sigma$ > -1 
Thus the limiting values of Poisson's ratio are -1 < $\sigma$ < 1/2

The correct option is (a)

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

The formula $Y=3B(1-2 \sigma)$ relates young's modulus and bulk's modulus with poisson's ratio. A theoretical physicist derives this formula incorrectly as $Y=3B(1-4 \sigma)$. According to this formula, what would be the theoretical limits of poisson's ratio:

  1. Poisson's ratio should be less than 1

  2. Poisson's ratio should be less than 0.5

  3. Poisson's ratio should be less than 0.25

  4. Poisson's ratio should be less than 0
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

In the formula derived by the student, in order that Y is positive, $\sigma<0.25$, else Y will be negative, which is not possible

Hence, poisson's ratio should be less than 0.25

The correct option is option(c)

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

The ice storm in the state of Jammu strained many wires to the breaking point. In a particular situation, the transmission towers are separated by $500\ m$ of wire. The top grounding wire $15^{o}$ from horizontal at the towers, and has a diameter of $1.5cm$. The steel wire has a density of $7860\ kg\ m^{-3}$. When ice (density $900\ kg\ m^{-3}$) built upon the wire to a diameter $10.0\ cm$, the wire snapped. What was the breaking stress (force/ unit area) in $N\ m^{-2}$ in the wire at the breaking point? You may assume the ice has no strength.

  1. $7.4\ \times 10^{7}\ N\ m^{-2}$

  2. $4.5\ \times 10^{8}\ N\ m^{-2}$

  3. $2.6\ \times 10^{6}\ N\ m^{-2}$

  4. $1.15\ \times 10^{7}\ N\ m^{-2}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The breaking stress is the force required to break the wire divided by its cross-sectional area. By calculating the weight of the ice and the wire, and considering the geometry, the stress is found to be 2.6 * 10^6 N/m^2.

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

A steel wire of length $30cm$ is stretched ti increase its length by $0.2cm$. Find the lateral strain in the wire if the poisson's ratio for steel is $0.19$ :

  1. $0.0019$

  2. $0.0008$

  3. $0.019$

  4. $0.008$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Poisson's ratio $=-\cfrac{\epsilon _{lateral}}{\epsilon _{Longtudinal}}$

$\epsilon _{longitudinal}=\cfrac{\triangle L}{L}=\cfrac{0.2}{20}$
$\therefore \epsilon _{lateral}=-\cfrac{0.2}{20}\times 0.19$
$=-0.0019$
$|\epsilon _{lateral}|=0.0019$

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

For a material $Y={ 6.6\times 10 }^{ 10 }\ { N/m }^{ 2 }$ and bulk modulus $K{ 11\times 10 }^{ 10 }\ { N/m }^{ 2 }$, then its Poisson'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

Given that,

Young’s modulus $Y=6.6\times {{10}^{10}}\,N/{{m}^{2}}$

Bulk modulus $B=11\times {{10}^{10}}\,N/{{m}^{2}}$

We know that,

  $ Y=3K\left( 1-2\mu  \right) $

 $ 6.6\times {{10}^{10}}=3\times 11\times {{10}^{10}}-66\times {{10}^{10}}\mu  $

 $ -\mu =\dfrac{\left( 6.6-33 \right)\times {{10}^{10}}}{66\times {{10}^{10}}} $

 $ \mu =0.4 $

Hence, the poisson’s ratio is $0.4$

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

The increase in the length of a wire on stretching is $0.025 \%$. If its Poisson's ratio is $0.4$, then the percentage decrease in the diameter is :

  1. $0.01$

  2. $0.02$

  3. $0.03$

  4. $0.04$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Suppose, D be the diameter of the wire Poissons ratio,  

$σ=\frac { lateral strain }{ longitudinal strain } $

 $σ=\frac { \frac { ΔD }{ D }  }{ \frac { ΔL }{ L }  } $

 $\frac { ΔL }{ L } =0.025$

 $σ=0.004$

 $σ=\frac { \frac { ΔD }{ D }  }{ \frac { 1 }{ 40 }  } $

 $\frac { ΔD }{ D } =\frac { 1 }{ 40 } \times 0.4=0.01$