Mechanical properties of solids practice · Mixed difficulty

Option D (Metals have larger values of Young’s modulus than elastomers) is the incorrect statement because metals are generally stiffer than elastomers, meaning they have a higher Young's modulus.

Option D (None of the above) is correct because Young's modulus is a material property and is not affected by the dimensions of the wire.

Option A ($Fl/2AL$) is correct because the elastic energy stored per unit volume is given by $\frac{1}{2} \times \text{{stress}} \times \text{{strain}}$.

Option C ($3.1\, \times \,{10^6}\,N{m^{ - 2}}$) is correct because the tensile stress is calculated by dividing the force (weight) by the area of the wire.

Option A (0%) is correct because a Poisson's ratio of 0.5 implies that the volume remains constant under longitudinal strain.

Option A is correct because steel is more elastic than rubber, and this is because for the same strain, steel requires more stress.

Option A (If both Assertion and Reason are true and the Reason is correct explanation of the Assertion) is correct because the spring constant is inversely proportional to the length of the wire, as derived from the given relation.

Option B (Stress) is correct because the modulus of elasticity is defined as the ratio of stress to strain, making it dimensionally equivalent to stress.

Option D (0.4) is correct because Poisson's ratio typically ranges from -1 to 0.5 for most materials.

Option C (Is equal to its pressure $p$) is correct because the bulk modulus at constant temperature (isothermal process) is equal to the pressure of the gas.

Option D is correct because the ratio of stress and strain is not always constant; it's only constant within the elastic limit, and the ratio is called the modulus of elasticity.

Option D (9) is correct because the stress is proportional to the linear dimension when density is constant.

Option A (If both A & R are true and the R is the correct explanation of the A) is correct because increasing temperature weakens intermolecular forces, decreasing the modulus of elasticity, and the asymmetric potential energy curve explains thermal expansion.

Option B (If both assertion and reason are true but reason is not the correct explanation of assertion) is correct because Hooke's law applies to small deformations, and elastomers are an exception, but the reason doesn't explain the assertion.

Option A (0.7) is correct because Poisson's ratio must lie between -1 and 0.5 theoretically, and practically between 0 and 0.5. 0.7 exceeds this limit.

Option D (Elastic after effect) is correct because it specifically describes the temporary delay in regaining the original configuration after removing a deforming force.

Option D ($\frac{{Fl}}{2}$) is correct because the work done in stretching a wire is equal to the potential energy stored, which is half the product of the force and the extension.

Option D is correct because the maximum load a wire can withstand depends on its cross-sectional area and material properties, not its length.

The correct answer is that liquids have no definite shape, which prevents them from having a Poisson's ratio.

Option A ($2 \times 10^{11}$) is correct because it is calculated using the formula for Young's modulus in terms of work done, force, length, and area.

Option C (If Assertion is true, but the Reason is false) is correct because the bulk modulus of gases increases with pressure, but the reason provided about temperature increase is not always true and not the primary explanation.

Option A (2.5) is correct because the longitudinal strain is calculated using Poisson's ratio and the percentage increase in volume.

Option B ($\sqrt{\frac{Y_{\text {iron }}}{Y_{\text {copper }}}}$) is correct because the ratio of diameters is inversely proportional to the square root of Young's modulus when tension and length change are the same.

Option A (Young’s modulus for a perfectly rigid body is zero) is correct because Young's modulus for a perfectly rigid body is infinite, not zero.

Option A (3600) is correct because it is the energy per unit volume calculated using the formula with Young's modulus and strain.

Option A (Statement I is true and statement II is true) is correct because both statements accurately describe stress and the origin of elasticity in solids.

Option A (Statement I is true and statement II is true) is correct because a perfectly plastic body has zero restoring force and therefore zero Young's modulus.

Option B (If both A $\& R$ are true but the R is not the correct explanation of the A) is correct because both the assertion and the reason are true statements, but the reason does not explain why the modulus of elasticity is independent of the dimensions of the body.

Option A (Uncompressible) is correct because if Poisson's ratio is -1/2, the bulk modulus becomes infinite, indicating an incompressible material.

Option C ($9 F$) is correct because the tensile force required to break a wire is proportional to the cross-sectional area, which is proportional to the square of the radius.