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

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:

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:

Dimensions of stress are:

Given below are two statements:$\newline$Assertion (A): The stretching of a spring is determined by the shear modulus of the material of the spring.$\newline$Reason (R): A coil spring of copper has more tensile strength than a steel spring of the same dimensions.$\newline$Choose the most appropriate answer:

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:

The maximum elongation of a steel wire of 1 m length if the elastic limit of steel and its Young’s modulus, respectively, are $8 \times 10^8$ N/m$^2$ and $2 \times 10^{11}$ N/m$^2$ is:

The quantities which have the same dimensions as those of solid angle are:

A metallic bar of Young’s modulus, $0.5 \times 10^{11}$ N/m$^2$ and coefficient of linear thermal expansion $10^{-5}$ °C$^{-1},$ length 1 m and area of cross-section $10^{-3}$ m$^2$ is heated from $0^\circ$C to $100^\circ$C without expansion or bending. The compressive force developed in it is: