The correct answer is: $${\sigma {\text{b}}}$$ = 6 N/mm2, $${\sigma {\text{s}}}$$ = 12 N/mm2.
The stress in a bar is given by the formula:
$$\sigma = \frac{F}{A}$$
where $F$ is the force applied to the bar, $A$ is the cross-sectional area of the bar, and $\sigma$ is the stress in the bar.
In this case, the force applied to the bar is $F = 1,00,000 N$, the cross-sectional area of the steel bar is $A_s = 3500 mm^2$, and the cross-sectional area of the brass bar is $A_b = 3000 mm^2$. The Young’s modulus of steel is $E_s = 0.2 MN/mm^2$, and the Young’s modulus of brass is $E_b = 0.1 MN/mm^2$.
The stress in the steel bar is:
$$\sigma_s = \frac{F}{A_s} = \frac{1,00,000 N}{3500 mm^2} = 28.57 N/mm^2$$
The stress in the brass bar is:
$$\sigma_b = \frac{F}{A_b} = \frac{1,00,000 N}{3000 mm^2} = 33.33 N/mm^2$$
Therefore, the stresses developed are:
$${\sigma {\text{b}}}$$ = 6 N/mm2, $${\sigma {\text{s}}}$$ = 12 N/mm2.
Here is a brief explanation of each option:
- Option A: ${\sigma {\text{b}}}$ = 10 N/mm2, ${\sigma {\text{s}}}$ = 20 N/mm2. This option is incorrect because the stress in the steel bar cannot be greater than the stress in the brass bar. The stress in a bar is proportional to its Young’s modulus, and the Young’s modulus of steel is greater than the Young’s modulus of brass. Therefore, the stress in the steel bar must be less than the stress in the brass bar.
- Option B: ${\sigma {\text{b}}}$ = 8 N/mm2, ${\sigma {\text{s}}}$ = 16 N/mm2. This option is incorrect because the stress in the steel bar cannot be less than the stress in the brass bar. The stress in a bar is proportional to its Young’s modulus, and the Young’s modulus of steel is greater than the Young’s modulus of brass. Therefore, the stress in the steel bar must be greater than the stress in the brass bar.
- Option C: ${\sigma {\text{b}}}$ = 6 N/mm2, ${\sigma {\text{s}}}$ = 12 N/mm2. This option is correct because the stress in the steel bar is greater than the stress in the brass bar, and the stress in each bar is proportional to its Young’s modulus.
- Option D: ${\sigma {\text{b}}}$ = 5 N/mm2, ${\sigma {\text{s}}}$ = 10 N/mm2. This option is incorrect because the stress in the steel bar cannot be less than the stress in the brass bar. The stress in a bar is proportional to its Young’s modulus, and the Young’s modulus of steel is greater than the Young’s modulus of brass. Therefore, the stress in the steel bar must be greater than the stress in the brass bar.