A body was subjected to two mutually perpendicular stresses of -6MPa and 24MPa respectively. What is the shear stress on the plane of pure shear?a)30 Mpab)12 Mpac)15 Mpad)9 MpaCorrect answer is option 'B'. Can you explain this answer?

Question

Answer

Shear stress is a measure of the force per unit area acting parallel to a given plane within a material. In pure shear, the stress is applied in such a way that one face of the material is fixed and the other face is subjected to equal and opposite forces in the perpendicular directions.

Given:
Stress in one direction = -6 MPa (negative sign indicates a compressive stress)
Stress in the perpendicular direction = 24 MPa

To find the shear stress on the plane of pure shear, we can use the formula for finding the resultant stress on an inclined plane:

σ = √(σ₁² + σ₂² - 2σ₁σ₂cos(2θ))

where σ₁ and σ₂ are the stresses in the two perpendicular directions, and θ is the angle between the plane and the direction of σ₁.

In this case, since the stresses are mutually perpendicular, θ = 90 degrees, and the formula simplifies to:

σ = √(σ₁² + σ₂²)

Now we can substitute the given values:

σ = √((-6 MPa)² + (24 MPa)²)
= √(36 MPa² + 576 MPa²)
= √(612 MPa²)
= 24.74 MPa

Therefore, the shear stress on the plane of pure shear is approximately 24.74 MPa.

Now we can compare this with the given options:
a) 30 MPa
b) 12 MPa
c) 15 MPa
d) 9 MPa

Since the calculated shear stress is not equal to any of the options, none of the options are correct. It is possible that there is an error in the question or the answer choices.

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