Which of the following is true for elastic potential energy density
Energy density $=$ $\frac{1}{2} \times {\rm{strain}} \times {\rm{stress}}$
Energy density $=$ ${{\rm{(strain)}}^2} \times {\rm{volume}}$
Energy density $=$ $strain$ $\times$ $volume$
Energy density $=$ $stress$ $\times$ $volume$
If one end of a wire is fixed with a rigid support and the other end is stretched by a force of $10 \,N,$ then the increase in length is $0.5\, mm$. The ratio of the energy of the wire and the work done in displacing it through $1.5\, mm$ by the weight is
When a $4\, kg$ mass is hung vertically on a light spring that obeys Hooke's law, the spring stretches by $2\, cms$. The work required to be done by an external agent in stretching this spring by $5\, cms$ will be ......... $joule$ $(g = 9.8\,metres/se{c^2})$
A wire of length $L$ and cross-sectional area $A$ is made of a material of Young's modulus $Y.$ It is stretched by an amount $x$. The work done is
$K$ is the force constant of a spring. The work done in increasing its extension from ${l_1}$ to ${l_2}$ will be
The work done per unit volume to stretch the length of area of cross-section $2 \,mm ^2$ by $2 \%$ will be ....... $MJ / m ^3$ $\left[Y=8 \times 10^{10} \,N / m ^2\right]$