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

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

  1. Increase

  2. Decrease

  3. Remains same

  4. Initially increases and then decreases
Reveal answer Fill a bubble to check yourself
B Correct answer
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)

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

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

  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
Reveal answer Fill a bubble to check yourself
B Correct answer
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

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

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

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

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

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

  4. $2.5 \times 10^{-3}$
Reveal answer Fill a bubble to check yourself
B Correct answer
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)

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.