On stretching a wire, the elastic energy stored per unit volume is
Medium
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(a) Energy stored per unit volume $=$ $\frac{1}{2}\left( {\frac{F}{A}} \right)\;\left( {\frac{l}{L}} \right)$ $=$ $\frac{{Fl}}{{2AL}}$
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$Assertion :$ Solids are least compressible and gases are most compressible.
$Reason :$ solids have definite shape and volume but gases do not have either definite shape or definite volume.
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 uniform metallic wire is elongated by $0.04\, m$ when subjected to a linear force $F$. The elongation, if its length and diameter is doubled and subjected to the same force will be ..... $cm .$
The strain-stress curves of three wires of different materials are shown in the figure. $P, Q$ and $R$ are the elastic limits of the wires. The figure shows that
A brass rod of length $2\,m$ and cross-sectional area $2.0\,cm^2$ is attached end to end to a steel rod of length $L$ and cross-sectional area $1.0\,cm^2$ . The compound rod is subjected to equal and opposite pulls of magnitude $5 \times 10^4\,N$ at its ends. If the elongations of the two rods are equal, then length of the steel rod $(L)$ is ........... $m$ $(Y_{Brass}=1.0\times 10^{11}\,N/m^2$ and $Y_{Steel} = 2.0 \times 10^{11}\,N/m^2)$
A copper solid cube of $60\,\, mm$ side is subjected to a pressure of $2.5 \times 10^7\, Pa$. If the bulk modulus of copper is $1.25 \times 10^{11}\, N/m^2$, the change in the volume of cube is