Elastic behaviour, stress-strain, Hooke's law, Young's, bulk and rigidity moduli

The maximum elongation of a steel wire of 1 m length if the elastic limit of steel and its Young's modulus, respectively, are \(8\times10^8\) N m\(^{-2}\) and \(2\times10^{11}\) N m\(^{-2}\), 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 L\(_1\) when mass M is suspended from its free end. The expression for Young's modulus is :

When a block of mass M is suspended by a long wire of length L, the length of the wire becomes \((L+l)\). The elastic potential energy stored in the extended wire is :

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 \(\Delta l\) 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', the fractional decrease in radius is :