NEET Physics Mechanical Properties Of Solids MCQs

A long, thin rod of length 'L' and radius 'r' is clamped at one end and subjected to a twisting couple at the other end. If the angle of twist is 'θ' and the rigidity modulus of the material is 'η', the maximum shearing stress developed in the rod is proportional to:

A wire of length L and cross-sectional area A is stretched by a force F. If its volume remains constant, what is the Poisson's ratio of the material of the wire?

The strain energy per unit volume of a stretched wire is given by:

A cylindrical rod of material A with Poisson's ratio $

u_A$is encased within a rigid cylindrical shell. When subjected to an axial compressive force, the lateral strain in material A is found to be zero. Now, the rigid shell is replaced by a shell made of material B with Poisson's ratio$

u_B$and the same axial force is applied. If the lateral strain in material A is now measured to be$\epsilon$, which of the following relationships must hold true?

A thin, square plate of side 'a' and thickness 't' (t << a) made of a material with Poisson's ratio $

u$is subjected to biaxial tensile stress$\sigma$in both x and y directions. Which expression correctly represents the fractional change in thickness ($\Delta t/t$) of the plate?

A long, thin wire of radius 'r' and length 'L' made of a material with Young's modulus 'E' and Poisson's ratio $

u$ is subjected to a tensile force 'F'. If the volume of the wire remains constant during the application of the force, what is the value of Poisson's ratio?

A cylindrical rod of material A is encased within a hollow cylindrical shell of material B. Both materials are perfectly bonded at their interface. When subjected to an axial compressive force, material A experiences a lateral strain of $\epsilon_A$. The Poisson's ratio of material A is $

u_A$and its Young's modulus is$E_A$. Material B has a Poisson's ratio of$

u_B$and a Young's modulus of$E_B$. Assuming the lateral strain in material B is identical to that of material A ($\epsilon_B = \epsilon_A$), and the axial strain in material B is negligible compared to material A, what is the ratio of the radial stress in material B to the radial stress in material A?

A wire of length $L$ and cross-sectional area $A$ is stretched by a force $F$. If the Young's modulus of the wire is $Y$, and the wire obeys Hooke's law within the elastic limit, the strain energy density stored in the wire is:

Which modulus describes a material's resistance to shearing stress?

A wire of length L and radius r is subjected to a tensile stress $\sigma$. If Young's modulus is Y and the Poisson's ratio is $

u$, the decrease in radius is given by: