What is called elastic energy density ? Write its formula and dimensional formula.

When strain is produced in a body within elastic limit, its internal energy

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

A stone of mass $20\, {g}$ is projected from a rubber catapult of length $0.1\, {m}$ and area of cross section $10^{-6} \,{m}^{2}$ stretched by an amount $0.04\, {m}$. The velocity of the projected stone is $....\,m\,/s.$ (Young's modulus of rubber $=0.5 \times 10^{9}\, {N} / {m}^{2}$ )

A block of mass $M$ is suspended from a wire of length $L$, area of cross-section $A$ and Young's modulus $Y$. The elastic potential energy stored in the wire is

When a force is applied on a wire of uniform cross-sectional area $3 \times {10^{ - 6}}\,{m^2}$ and length $4m$, the increase in length is $1\, mm.$ Energy stored in it will be $(Y = 2 \times {10^{11}}\,N/{m^2})$