NEET Mechanical Properties of Solids Previous Year Questions with Solutions

Up to the elastic limit, deformation is completely reversible, and Hooke’s law holds rigorously. Young’s modulus Y is defined as the ratio of tensile stress σ to tensile strain ε:

To find the maximum elongation ΔL_max without exceeding the elastic limit, we use the maximum allowable stress σ_max:

Substituting σ_max = 8 × 10⁸ N m⁻², L = 1 m, and Y = 2 × 10¹¹ N m⁻²:

Since 1 m = 1000 mm:

When an external deforming force is applied to a body, an internal restoring force equal in magnitude and opposite in direction develops within the material across every plane of cross-section. Stress σ is defined as this internal restoring force per unit area:

For a wire of negligible mass suspended from a rigid ceiling and carrying a weight W at its free end, make an imaginary horizontal cut at any point along the wire. For the lower portion to remain in static equilibrium, the internal tension T across the cross-sectional area A must balance the weight W:

Substituting the internal restoring tension into the stress formula:

When mass $$M$$ is suspended from the free end, the deforming tensile force acting across the cross-sectional area $$A$$ of the wire is its weight: $$F = Mg$$ $$\text{Longitudinal Stress} = \frac{F}{A} = \frac{Mg}{A}$$.

The initial length of the wire is $$L$$, and the stretched final length is $$L_1$$. Change in length (elongation): $$\Delta L = L_1 - L$$ $$\text{Longitudinal Strain} = \frac{\Delta L}{L} = \frac{L_1 - L}{L}$$.

Young's modulus ($$Y$$) is defined as the ratio of longitudinal stress to longitudinal strain within the elastic limit: $$Y = \frac{\text{Stress}}{\text{Strain}} = \frac{\frac{Mg}{A}}{\frac{L_1 - L}{L}}$$.

Inverting the denominator fraction yields: $$Y = \frac{Mg \cdot L}{A(L_1 - L)}$$. Matches Option 4.