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Two steel wires having same length are suspended from a ceiling under the same load. If the ratio of their energy stored per unit volume is $1: 4,$ the ratio of their diameters is
On increasing the length by $0.5\, mm$ in a steel wire of length $2\, m$ and area of cross-section $2\,m{m^2}$, the force required is $[Y$ for steel$ = 2.2 \times {10^{11}}\,N/{m^2}]$
A block of weight $100 N$ is suspended by copper and steel wires of same cross sectional area $0.5 cm ^2$ and, length $\sqrt{3} m$ and $1 m$, respectively. Their other ends are fixed on a ceiling as shown in figure. The angles subtended by copper and steel wires with ceiling are $30^{\circ}$ and $60^{\circ}$, respectively. If elongation in copper wire is $\left(\Delta \ell_{ C }\right)$ and elongation in steel wire is $\left(\Delta \ell_{ s }\right)$, then the ratio $\frac{\Delta \ell_{ C }}{\Delta \ell_{ S }}$ is. . . . . .
[Young's modulus for copper and steel are $1 \times 10^{11} N / m ^2$ and $2 \times 10^{11} N / m ^2$ respectively]
The stress versus strain graphs for wires of two materials $A$ and $B$ are as shown in the figure. If $Y_A$ and $Y_B$ are the Young's modulus of the materials, then
An aluminium rod with Young's modulus $Y =7.0$ $\times 10^{10} N / m ^2$ undergoes elastic strain of $0.04 \%$. The energy per unit volume stored in the rod in SI unit is:
The following four wires of length $L$ and radius $r$ are made of the same material. Which of these will have the largest extension, when the same tension is applied?
A steel rod of length $\ell$, cross sectional area $A$, young's modulus of elasticity $Y$, and thermal coefficient of linear expansion $'a'$ is heated so that its temperature increases by $t\,^oC$. Work that can be done by rod on heating will be