Mechanical Properties of Solids PYQs

Match List I with List II: Choose the correct answer from the options given below:

The maximum elongation of a steel wire of 1 m length if the elastic limit of steel and its Young modulus, respectively, are 8 × 10⁸ N m⁻² and 2 × 10¹¹ N m⁻², is:

A metallic bar of Young’s modulus 0.5 × 10¹¹ N m⁻² and coefficient of linear expansion 10⁻⁵ °C⁻¹, length 1 m and area of cross-section 10⁻³ m² is heated from 0°C to 100°C without expansion or bending. The compressive force developed in it is:

Let a wire be suspended from the ceiling (rigid support) and stretched by a weight W attached at its free end. The longitudinal stress at any point of cross-sectional area A of the wire is :

Given below are two statements: One is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): The stretching of a spring is determined by the shear modulus of the material of the spring. Reason (R): A coil spring of copper has more tensile strength than a steel spring of same dimensions. In the light of the above statements, choose the most appropriate answer from the options given below.

A wire of length L, area of cross section A is hanging from a fixed support. The length of the wire changes to L₁ when mass M is suspended from its free end. The expression for Young’s modulus is:

The stress-strain curves are drawn for two different materials X and Y. It is observed that the ultimate strength point and the fracture point are close to each other for material X but are far apart for material Y. We can say that materials X and Y are likely to be (respectively),

Two wires are made of the same material and have the same volume. The first wire has cross-sectional area A and the second wire has cross-sectional area 3A. If the length of the first wire is increased by Δl on applying a force F, how much force is needed to stretch the second wire by the same amount?

The bulk modulus of a spherical object is $B$. If it is subjected to uniform pressure $p$, then the fractional decrease in radius is:

The Young's modulus of steel is twice that of brass. Two wires of the same length and same cross-sectional area, one of steel and another of brass, are suspended from the same roof. If the lower ends of the wires are to be at the same level, the weights added to the steel and brass wires must be in the ratio:

Copper of fixed volume 'V; is drawn into a wire of length 'l'. When this wire is subjected to a constant force 'F', the extension produced in the wire is '$\Delta$l'. Which of the following graphs is a straight line?