GATE Mechanical Engineering (ME) 2018 Shift 1 Solved Paper

General equation learned for
Normal stress on inclined plane
σn=‌

σx+σy

2

+‌

σx−σy

2

‌cos‌2‌θ+τxy‌sin‌2‌θ
And shear stress for inclined plane
τn=−‌

σx−σy

2

‌sin‌2‌θ+τxy‌cos‌2‌θ
when θ is measured clockwise from left face.
Hence θ must be replaced by (−θ) in above equations and σy=0,τxy=0
σn=‌

σx

2

+‌

σx

2

‌cos‌2(−30)+0
σn=‌

4

2

+‌

4

2

‌cos(−60)
σn=3MPa
τn=−‌

σx

2

‌sin‌2(−θ)
τn=‌

σx

2

‌sin(2θ)
τn=‌

4

2

‌sin(60)
τn=1.73
Since both the stress exceeds the given limits, answer is option (C).