Mechanical properties of solids practice · Medium

Option D (8.8 N) is correct because the increase in tension is calculated considering both the applied force and the thermal stress due to temperature change.

Option B ($\frac{{{S^2}}}{{2Y}}$) is correct because it represents the elastic energy stored per unit volume, derived from the formula involving stress and Young's modulus.

Option A (4 rad/sec) is correct because the maximum angular velocity is calculated using the breaking stress, area, mass, and length.

Option C (Stress) is correct because stress is defined as the restoring force per unit area within a deformable body.

Option C ($K = \frac{{Y\eta }}{{9\eta - 3Y}}N/{m^2}$) is the correct relation between Young’s modulus, bulk modulus and modulus of rigidity.

The correct answer is D (Tensor) because stress is a tensor quantity that describes forces acting on a cross-sectional area.

Option D (Decrease by 0.75 mL) is correct because the volume of water decreases under pressure, and the calculated decrease is 0.75 mL based on the given compressibility and pressure.

Option B (Same) is correct because the load a wire can hold depends on the breaking stress of the material and the cross-sectional area, not the length of the wire.

Option D (80 kg-wt) is correct because the breaking force is proportional to the cross-sectional area, which is proportional to the square of the diameter.

Option C ($1 \times {10^{12}}$) is correct because it is the calculated bulk modulus of the rubber based on the given pressure and volume reduction.

Option A ($1 \times {10^{ - 4}}$) is correct because strain is defined as the change in length divided by the original length, which is 0.01% or 0.0001.

Option B (If both Assertion & Reason are True but Reason is not a correct explanation of the Assertion) is correct because elastic restoring forces can be conservative, and hysteresis explains the difference in strain for the same stress during loading and unloading, but hysteresis doesn't explain why restoring forces *may* be conservative.

Option D ($\mathrm{[}\,\mathrm{M}\,{\mathrm{L}^{ - 1}}\,{\mathrm{T}^{ - 2}}\,\mathrm{]}$) is correct because stress is force per unit area, and the dimensions of force are $[MLT^{-2}]$ and area are $[L^2]$, so stress is $[ML^{-1}T^{-2}]$.

Option D ($\frac{{Fl}}{2}$) is correct because the work done in stretching a wire is given by half the product of force and extension.

Option D (Rubber, glass, copper, steel) is correct because it lists the materials in order of increasing Young's modulus (coefficient of elasticity).

Option A (0.7) is the correct answer because Poisson's ratio is generally between 0 and 0.5 for most materials, and 0.7 exceeds this range.

Option B (${10^4}\,\mathrm{N}$) is correct because the force required is calculated using the formula $F = YA\alpha \Delta T$, where Y is Young's modulus, A is the area, $\alpha$ is the coefficient of linear expansion, and $\Delta T$ is the change in temperature.

Option C (Tensile stress and longitudinal strain) is correct because Young's modulus is defined as the ratio of tensile stress to longitudinal strain.

Option B is correct because Young's modulus is defined as the stress required to produce unit strain.

Option A is correct because Invar has a very low coefficient of thermal expansion, making it suitable for balance wheels in watches to maintain constant time.

Option C (4 cm) is correct because elongation is inversely proportional to the square of the diameter.

Option C ($4\,F$) is correct because the force needed to break a wire is proportional to the cross-sectional area, which is proportional to the square of the radius.

Option D ($\frac{1}{2}y{x^2}$) is correct because it represents the energy stored per unit volume in a wire with longitudinal strain x and Young's modulus y.

Option D is correct because Statement I is false as the ivory ball will bounce higher due to its higher elasticity, and Statement II is false because ivory and wet-clay do not have the same elasticity.

Option A ($y\frac{{\Delta l}}{l}$) is correct because thermal stress is given by Young's modulus times the strain.

Option A is correct because a perfectly rigid body does not deform under any stress, thus its Young's modulus is infinite.

Option C is correct. Young's modulus is calculated using the formula Y = (F/A) / (ΔL/L), where the length doubles, meaning ΔL = L.

Option B (Second term represents the attractive part of the potential) is correct because the negative sign in front of the second term indicates an attractive force as the distance R increases.

Option A ($k={YA} / {L}$) is correct because it represents the spring constant derived from Young's modulus definition.

Option A (Hooke’s law is applicable only within elastic limit) is correct because Hooke's law is only valid within the elastic limit of a material.