Tag: properties of material substances

Questions Related to properties of material substances

The change in unit volume of a material under tension with increase in its poisson's ratio will be

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

  1. Increase

  2. Decrease

  3. Remains same

  4. Initially increases and then decreases

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Correct Option: B
Explanation:

The poisson's ratio is related to modulus of elasticity as $Y = 3B(1-2 \sigma)$. Since stress is same for Y and B, we get, $dL/L=dV/3V(1-2 \sigma) \implies dV=3V (dL/L)(1-2 \sigma)$
As $\sigma$ is increased, $dV$ decreases. 

The correct option is (b)

The formula relating youngs modulus (Y), rigidity modulus (n) and Poisson's ratio ($\sigma$) is 

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

  1. $Y=2n(1- \sigma)$

  2. $Y=2n(1+\sigma)$

  3. $Y=n(1- 2\sigma)$

  4. $Y=n(1+2 \sigma)$

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Correct Option: B
Explanation:

Young's modulus and rigidity modulus can be related to poisson's ratio as $Y=2n(1+\sigma)$

The correct option is (b)

A student measures the poisson's ratio to be greater than 1 in an experiment. The meaning of this statement would be

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

  1. An increase in length would also result in decrease in area of cross section of the wire

  2. An increase in length would also result in increase in area of cross section of the wire

  3. An decrease in length would also result in decrease in area of cross section of the wire

  4. An increase in length will not change the area of cross section of the wire

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Correct Option: B
Explanation:

Poisson's ratio = change in area /  change in length. If poisson's ratio >1, then change in area > change in length. Thus area expands when length increases

The option (b) is the correct option

The formula that relates Bulk's modulus with poisson's ratio is 

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

  1. $Y=3B(1+2 \sigma)$

  2. $Y=3B(1- \sigma)$

  3. $Y=3B(1-2 \sigma)$

  4. $Y=3B(1+ \sigma)$

Show answer
Correct Option: C
Explanation:

The formula relating young's modulus and bulk's modulus with poisson's ratio is $Y=3B(1-2 \sigma)$

The option (c) is the correct option

A copper wire 3 m long is stretched to increase its length by 0.3 cm. Find the lateral strain produced in the wire , if poisson's ratio for copper is 0.25

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

  1. $5 \times 10^{-4}$

  2. $2.5 \times 10^{-4}$

  3. $5 \times 10^{-3}$

  4. $2.5 \times 10^{-3}$

Show answer
Correct Option: B
Explanation:

Longitudinal strain = 0.3 cm/3 m = 0.0001

Lateral strain = poisson's ratio x longitudinal strain =$ 0.25 \times 0.0001 = 2.5 \times 10^{-4}$

The correct option is (b)

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

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

  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

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Correct Option: A
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)

The formula that relates all three elastic constants is 

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

  1. 9/Y = 3/n - 1/B

  2. 9/Y = 3/n + 1/B

  3. 9/Y = 3/n + 2/B

  4. 9/Y = 3/n - 2/B

Show answer
Correct Option: B
Explanation:

The formula that relates all three elastic constants is 9/Y = 3/n + 1/B

The correct option is (b)

What is the poisson's ratio of a wire, whose Young's modulus and Bulk's modulus are equal

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

  1. 1/2

  2. 2/3

  3. 1/3

  4. 1/4

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Correct Option: C
Explanation:

We know that $Y=3B(1-\sigma)$. Substituting, Y=B, we get, $1/3=1-2 \sigma$ or poisson's ratio = 1/3

The correct option is (c)

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:

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

  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

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Correct Option: C
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)

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.

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

  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. $1.15\ \times 10^{7}\ N\ m^{-2}$

Show answer
Correct Option: C