An elastic material of Young's modulus $Y$ is subjected to a stress $S$. The elastic energy stored per unit volume of the material is
$\frac{{2Y}}{{{S^2}}}$
$\frac{{{S^2}}}{{2Y}}$
$\frac{S}{{2Y}}$
$\frac{{{S^2}}}{Y}$
Two wires $A$ and $B$ of same material have radii in the ratio $2: 1$ and lengths in the ratio $4: 1$. The ratio of the normal forces required to produce the same change in the lengths of these two wires is .......
A rod of length $l$ and area of cross-section $A$ is heated from $0°C$ to $100°C$. The rod is so placed that it is not allowed to increase in length, then the force developed is proportional to
A wire elongates by $l$ $mm$ when a load $W$ is hanged from it. If the wire goes over a pulley and two weights $W$ each are hung at the two ends, the elongation of the wire will be (in $mm$)
The ratio of diameters of two wires of same material is $n : 1$. The length of wires are $4\, m$ each. On applying the same load, the increase in length of thin wire will be
If the length of a wire is made double and radius is halved of its respective values. Then, the Young's modules of the material of the wire will :