The State of stress at a point, for a body in place stress,

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The State of stress at a point, for a body in place stress, is shown in the figure below. If the minimum principal stress is 10 kPa, then the normal stress σ_s (in kPa) is

1. 9.45
2. 18.88
3. 37.78
4. 75.50

Correct Option: C

σ_x = 100 kPa, τ_xy = 50 kPa
Minimum principal stress

By squaring

2500 +	σ_y²	- 50σ_y + 2500 = 1600 +	σ_y²	+ 40σ_y
	4		4

∴ 90 σ_y = 3400
σ_y = 37.78 MPa