The problem describes a lamina subjected to a plane stress condition, with stresses applied at $60 \, \text{MPa}$ and $100 \, \text{MPa}$. We need to check which of the given options regarding the normal stress on planes MN and the plane perpendicular to MN are correct.

To analyze the stresses on plane MN, we can apply the equations of plane stress transformation. Specifically, the normal stress $\sigma_n$ and shear stress $\tau_n$ on a plane at an angle $\theta$ to the x-axis are given by:

$\sigma_{\text{normal}} = \sigma_x \cos^2(\theta) + \sigma_y \sin^2(\theta) + 2\tau_{xy} \sin(\theta) \cos(\theta)$ $\sigma_{\text{shear}} = (\sigma_y - \sigma_x) \sin(\theta) \cos(\theta) + \tau_{xy} (\cos^2(\theta) - \sin^2(\theta))$

Here:

• $\sigma_x = 100 \, \text{MPa}$ (the normal stress along the x-axis)
• $\sigma_y = 60 \, \text{MPa}$ (the normal stress along the y-axis)
• $\tau_{xy} = 0 \, \text{MPa}$ (as no shear stress is given)
• $\theta = 30^\circ$ (angle of MN from the horizontal axis)

Let's calculate the normal stresses for the planes MN and the plane perpendicular to MN.

I'll work through the math to determine which options are correct.The normal stresses calculated are as follows:

• The normal stress on plane MN is approximately $90 \, \text{MPa}$.
• The normal stress on the plane perpendicular to MN is approximately $70 \, \text{MPa}$.

Now, let's analyze the given options based on these results:

• (A) Normal stress in plane MN is $60 \, \text{MPa}$ (Tensile): This is incorrect, as the normal stress on plane MN is $90 \, \text{MPa}$, not $60 \, \text{MPa}$.
• (B) Normal stress in plane perpendicular to MN is $20 \, \text{MPa}$ (Compressive): This is incorrect, since the normal stress perpendicular to MN is approximately $70 \, \text{MPa}$.
• (C) Normal stress in plane MN is $75 \, \text{MPa}$ (Tensile): This is incorrect, the actual stress is $90 \, \text{MPa}$.
• (D) Normal stress in plane perpendicular to MN is $35 \, \text{MPa}$ (Compressive): This is incorrect, as the stress is $70 \, \text{MPa}$.

Thus, none of the options provided are correct.

Would you like more details or have any questions?

Here are five related questions to expand your understanding:

1. How does shear stress influence the normal stress on an inclined plane?
2. What are Mohr's circle representations for plane stress problems?
3. How do we calculate the shear stress on a plane at an angle $\theta$?
4. Why do we need to use transformation equations for stress analysis?
5. What happens if there is a non-zero shear stress $\tau_{xy}$?

Tip: Plane stress problems are easier to visualize if you use Mohr's circle, which graphically represents stress transformations.