Mechanical Properties of Solids

The Young's modulus of steel is twice that of brass. Two wires of same length and of same area of cross-section, one of steel and another of brass are suspended from the same roof. If we want the lower ends of the wires…

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…

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.…

An elastic spring under tension of $3 \mathrm{~N}$ has a length $a$. Its length is $b$ under tension $2 \mathrm{~N}$. For its length $(3 a-2 b)$, the value of tension will be______$\mathrm{N}$?

Two separate wires $A$ and $B$ are stretched by $2\mathrm{mm}$ and $4\mathrm{mm}$ respectively, when they are subjected to a force of $2N.$Assume that both the wires are made up of same material and the radius of wire…

When a rubber ball is taken to a depth of _______$m$ in deep sea, its volume decreases by$0.5%$ (The bulk modulus of rubber $=9.8\times\,10^{8}Nm^{-2}$Density of sea water $=10^{3}\mathrm{kg}m^{-3}$,$g=9.8ms^{-2}$)

A metal wire of length $0.5m$ and cross-sectional area $10^{-4}m^{2}$ has breaking stress $5\times\,10^{8}Nm^{-2}$. A block of $10\mathrm{kg}$ is attached at one end of the string and is rotating in a horizontal circle.…

The volume contraction of a solid copper cube of edge length 10 cm , when subjected to a hydraulic pressure of $7 \times 10^6 \mathrm{~Pa}$, would be ____ $\mathrm{mm}^3$. (Given bulk modulus of copper $=1.4 \times…

A sample of a liquid is kept at 1 atm. It is compressed to 5 atm which leads to change of volume of $0.8 \mathrm{~cm}^3$. If the bulk modulus of the liquid is 2 GPa , the initial volume of the liquid was _______ litre.…

A uniform wire of length $l$ of weight $w$ is suspended from the roof with a weight of $W$ at the other end. The stress in the wire at $\dfrac{l}{3}$ distance from the top is $\left(\dfrac{W}{A} +…

A steel wire of length 2 m and Young's modulus $2.0 \times 10^{11} \mathrm{Nm}^{-2}$ is stretched by a force. If Poisson ratio and transverse strain for the wire are 0.2 and $10^{-3}$ respectively, then the elastic…

The load versus elongation graphs for four wires of same length and made of the same material are shown in the figure. The thinnest wire is represented by the line