Grade 11 : Physics - Solids (Set 1)

Explanation: Stress is defined as the internal restoring force per unit cross-sectional area. Formula: $\text{Stress} = \frac{F}{A}$.

Explanation: Young's modulus is the ratio of stress (in $\text{N/m}^2$) to strain (dimensionless). Thus, its SI unit is $\text{N/m}^2$ or Pascal ($\text{Pa}$).

Explanation: Hooke's law states that for small deformations within the elastic limit, stress is directly proportional to strain ($\text{Stress} \propto \text{Strain}$).

Explanation: Strain is given by $\text{Strain} = \frac{\Delta L}{L} = \frac{1.0 \times 10^{-3}m}{2.0m} = 5.0 \times 10^{-4}$.

Explanation: Bulk modulus measures a fluid or solid's resistance to uniform volume reduction: $B = -\frac{\Delta P}{\Delta V / V}$.

Explanation: $\text{Stress} = \frac{F}{A} = \frac{200\text{ N}}{4.0 \times 10^{-4}m^2} = 5.0 \times 10^5\text{ Pa}$.

Explanation: Both Young's modulus and pressure are force per unit area, sharing the dimensional formula $[M L^{-1} T^{-2}]$.

Explanation: Compressibility $k$ is defined as the inverse of Bulk Modulus $B$, i.e., $k = \frac{1}{B}$.

Explanation: Shearing strain involves a change in shape of the body without any change in its volume.

Explanation: Elastic potential energy per unit volume is $u = \frac{1}{2} \times \text{Stress} \times \text{Strain}$.

Explanation: Young's modulus depends only on the material, not on dimensions. Since both wires are steel, the ratio is $1 : 1$.

Explanation: Steel requires a much higher stress for the same strain compared to rubber, meaning steel has a higher Young's modulus and is more elastic.

Explanation: Poisson's ratio is $\sigma = -\frac{\text{Lateral strain}}{\text{Longitudinal strain}}$.

Explanation: Theoretically, Poisson's ratio ranges from -1 to +0.5. In practice, it is positive for most engineering materials (0 to 0.5).

Explanation: Work stored $U = \frac{1}{2} F \Delta L = 0.5 \times 100 \times (0.5 \times 10^{-3}) = 0.025\text{ J}$.

Explanation: Elastic fatigue describes the temporary weakening of a material's elastic response caused by repeated cyclic loading.

Explanation: A perfectly plastic material exhibits zero restoring force and remains completely deformed once deforming forces cease.

Explanation: Breaking stress is an intrinsic material property. While breaking load depends on area, breaking stress depends solely on material type.

Explanation: Shearing strain $\theta = \frac{\Delta x}{L} = \frac{0.002m}{0.1m} = 0.02$.

Explanation: Materials capable of being stretched to large strains (several hundred percent) within their elastic range are classified as elastomers.