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

A brass rod of cross-sectional area $1\,c{m^2}$ and length $0.2\, m$ is compressed lengthwise by a weight of $5\, kg$. If Young's modulus of elasticity of brass is $1 \times {10^{11}}\,N/{m^2}$ and $g = 10\,m/{\sec ^2}$, then increase in the energy of the rod will be

The work done in increasing the length of a $1$ $metre$ long wire of cross-section area $1\, mm^2$ through $1\, mm$ will be ....... $J$ $(Y = 2\times10^{11}\, Nm^{-2})$

If $x$ longitudinal strain is produced in a wire of Young's modulus $y,$ then energy stored in the material of the wire per unit volume is

A wire suspended vertically from one of its ends is stretched by attaching a weight of $200\, N$ to the lower end. The weight stretches the wire by $1\, mm$ Then the elastic energy stored in the wire is ........ $J$

A wire is suspended by one end. At the other end a weight equivalent to $20\, N$ force is applied. If the increase in length is $1.0\, mm,$ the ratio of the increase in energy of the wire to the decrease in gravitational potential energy when load moves downwards by $1\, mm,$ will be