Physics · Mechanical Properties Of Solids · NEET
Both are the same thing for small angles. Shear strain is defined as the sideways displacement Δx divided by the height L of the block: shear strain = Δx/L. From the geometry of the tilted block, Δx/L is exactly tanθ, where θ is the angle the side tilts from its original vertical position. Since θ in NEET problems is very small, tanθ ≈ θ (in radians). So shear strain = Δx/L = tanθ ≈ θ. All three expressions are accepted.
By definition shear strain = Δx/L. Look at the tilted block: the top face moves sideways by Δx while the height stays L. The tilt angle θ satisfies tanθ = opposite/adjacent = Δx/L. So the exact value of shear strain is tanθ. We write tanθ ≈ θ only because θ is small (for θ = 10°, tanθ and θ differ by just about 1%). So θ is an approximation; tanθ = Δx/L is exact.
The direction of the force is the key difference. In tensile/longitudinal stress the two forces act perpendicular to (normal to) the face, so the body stretches along the force. In shearing stress the two equal and opposite forces act parallel (tangential) to the face, so opposite faces slide past each other and the shape changes (not the volume). Formula is F/A in both cases, but for shear, F is the tangential force and A is the area parallel to that force.
The force parallel (tangential) to the surface gives shearing stress. That is why it is also called tangential stress. If the force were perpendicular to the face it would produce longitudinal (tensile or compressive) stress instead. In NEET questions, look at the arrow direction: force along the surface means shear; force into or out of the surface means longitudinal.
No. Shear strain = Δx/L is a ratio of two lengths (metre / metre), so the units cancel out. It is a pure number and is dimensionless, exactly like every other kind of strain. Only the stress carries units (N/m² or pascal). This is a common trap: strain never has units, stress always does.
They have the same formula (force ÷ area) and the same SI unit (N/m² or pascal) and the same dimensions [ML⁻¹T⁻²], but they are physically different. Pressure is a force acting perpendicular to a surface (like a fluid pushing all around). Shearing stress is a force acting parallel to (along) the surface. Same units, different direction of the force.
Given below are two statements. Statement I: The stretching of a coil spring is determined by the shear modulus of the material of the spring. Statement II: A coil spring of copper has more tensile strength than a steel spring of same dimensions. Choose the most appropriate answer.
Try the real previous-year questions from this chapter — each with the answer and a full solution.
Shearing stress = tangential force / area = F/A (unit N/m² or Pa). Shear strain = Δx/L = tanθ ≈ θ, a dimensionless number, where Δx is the sideways shift of the top face and L is the height.
Shear modulus G = shearing stress / shearing strain = (F/A) / (Δx/L) = FL / (A·Δx). It can also be written G = (F/A)/θ. Its SI unit is N/m² (Pa). For most materials G is about Y/3, where Y is Young's modulus.
No. Shear modulus is relevant only for solids, because only solids have a fixed shape to resist sideways sliding. Liquids and gases flow when a tangential force is applied, so they cannot sustain a static shearing stress. This is why Young's and shear modulus apply only to solids.
When you pull a coil spring, the coils uncoil slightly, which twists the wire of the spring. Twisting is a shear deformation of the wire, so the spring's behaviour depends on the shear modulus of the wire material, not on Young's modulus.
Press a thick book flat with your hand and push the top cover sideways while the bottom stays fixed. The pages slide over each other and the book tilts by an angle θ. That tilt is the shear strain, equal to Δx/L = tanθ ≈ θ.
