Mechanical Properties of Solids

Two blocks of mass $2\mathrm{kg}$ and$4\mathrm{kg}$ are connected by a metal wire going over a smooth pulley as shown in figure. The radius of wire is$4.0\times\,10^{-5}m$and Young's modulus of the metal…

The density and breaking stress of a wire are $6 \times 10^4 \mathrm{~kg} / \mathrm{m}^3$ and $1.2 \times 10^8 \mathrm{~N} / \mathrm{m}^2$ respectively. The wire is suspended from a rigid support on a planet where…

The elastic behaviour of material for linear stress and linear strain, is shown in the figure. The energy density for a linear strain of $5\times\,10^{-4}$ is _____ $\mathrm{kJ}m^{-3}$. Assume that material is elastic…

Two blocks of masses $3\mathrm{kg}$ and $5\mathrm{kg}$ are connected by a metal wire going over a smooth pulley. The breaking stress of the metal is $\frac{24}{\pi\,}\times\,10^{2}Nm^{-2}$. What is the minimum radius of…

A uniform heavy rod of mass $20\mathrm{kg}$. Cross sectional area $0.4m^{2}$ and length $20m$ is hanging from a fixed support. Neglecting the lateral contraction, the elongation in the rod due to its own weight is…

Two slabs with square cross section of different materials $(1,2)$ with equal sides $(l)$ and thickness $\mathrm{d}_1$ and $\mathrm{d}_2$ such that $\mathrm{d}_2=2 \mathrm{~d}_1$ and $l \gt \mathrm{d}_2$. Considering…

A body of mass $m=10kg$ is attached to one end of a wire of length $0.3m$. What is the maximum angular speed (in $rads^{-1}$) with which it can be rotated about its other end in a space station without breaking the…

Wires $W_{1}$ and $W_{2}$ are made of same material having the breaking stress of $1.25\times\,10^{9}Nm^{-2}.W_{1}$ and $W_{2}$ have cross-sectional area of $8\times\,10^{-7}m^{2}$ and $4\times\,10^{-7}m^{2}$,…

A steel wire of length $3.2m\left(Y_{S}=2.0\times\,10^{11}Nm^{-2}\right)$ and a copper wire of length $4.4m\left(Y_{C}=1.1\times\,10^{11}Nm^{-2}\right)$ , both of radius $1.4\mathrm{mm}$are connected end to end. When…

In an experiment to determine the Young's modulus, steel wires of five different lengths ($1,2,3,4$and $5$) but of same cross-section $\left(2\mathrm{mm}^{2}\right)$ were taken and curves between extension and load were…

A uniform metallic wire is elongated by $0.04m$ when subjected to a linear force $F.$The elongation, if its length and diameter is doubled and subjected to the same force will be _________$\mathrm{cm}.$

One end of a metal wire is fixed to a ceiling and a load of $2\mathrm{kg}$ hangs from the other end. A similar wire is attached to the bottom of the load and another load of $1\mathrm{kg}$ hangs from this lower wire.…