Poisson's Effect

Q. Which is correct relation. ($\sigma$ is Poisson's Ratio, Y is the young's Modulus)

1. Y $<\sigma$
2. Y $>\sigma$
3. Y$=\sigma$
4. $\sigma =+1$

Q. A metal wire is stretched by a load. Then the fractional change in its volume $\frac{\Delta V}{V}$ is proportional to

1. $\frac{\Delta L}{L}$
2. ${\left(\frac{\Delta L}{2}\right)}^2$
3. $\sqrt{\frac{\Delta L}{L}}$
4. ${\left(\frac{\Delta L}{L}\right)}^3$

Q. A steel wire of cross sectional area $0.05{\text{cm}}^2$ is under a tension of $15\text{N}$. Find the decrease in the cross-sectional area. Young's modulus of steel = $2\times {10}^{11}{\text{N/m}}^2$ and Poisson's ratio = $0.3$.

1. $40\times {10}^{-8}{\text{cm}}^2$
2. $50\times {10}^{-8}{\text{cm}}^2$
3. $45\times {10}^{-8}{\text{cm}}^2$
4. $22.5\times {10}^{-8}{\text{cm}}^2$

Q. Poisson's ratio is the ratio of lateral strain to the longitudinal strain.

1. True
2. False

Q. A compressive force is applied to a uniform rod of rectangular cross-section so that its length decreases by 1%. If the Poisson's ratio for the material of the rod is $0.2$, then the volume approximately decreases by (in percentage).

Q. For the cube of given dimensions which is fixed at the bottom and acted upon by the force as shown in figure, identify the correct statement(s).
[Poisson's ratio $=0.8$ and Young's modulus $=2\times {10}^{11}{\text{N/m}}^2$]

1. Normal stress is $25\sqrt{3}{\text{N/m}}^2$
2. Shear stress is $25{\text{N/m}}^2$
3. Longitudinal strain is $12.5\sqrt{3}\times {10}^{-11}$
4. Magnitude of lateral strain is $10\sqrt{3}\times {10}^{-11}$

Q. For the cube of given dimensions which is fixed at the bottom and acted upon by the force as shown in figure, identify the correct statement(s).
[Poisson's ratio $=0.8$ and Young's modulus $=2\times {10}^{11}{\text{N/m}}^2$]

1. Normal stress is $25\sqrt{3}{\text{N/m}}^2$
2. Shear stress is $25{\text{N/m}}^2$
3. Longitudinal strain is $12.5\sqrt{3}\times {10}^{-11}$
4. Magnitude of lateral strain is $10\sqrt{3}\times {10}^{-11}$

Q. For the cube of given dimensions which is fixed at the bottom and acted upon by the force as shown in figure, identify the correct statement(s).
[Poisson's ratio $=0.8$ and Young's modulus $=2\times {10}^{11}{\text{N/m}}^2$]

1. Normal stress is $25\sqrt{3}{\text{N/m}}^2$
2. Shear stress is $25{\text{N/m}}^2$
3. Longitudinal strain is $12.5\sqrt{3}\times {10}^{-11}$
4. Magnitude of lateral strain is $10\sqrt{3}\times {10}^{-11}$