What is called elastic potential energy ? Write its different formulas.

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Two wires of the same material (Young's modulus  $Y$ ) and same length $L$  but radii  $R$  and  $2R$  respectively are joined end to end and a weight  $W$  is suspended from the combination as shown in the figure. The elastic potential energy in the system is

 A uniform metal rod of  $2\,\,mm^2$ cross section fixed between two walls is heated from $0\,^oC$ to $20\,^oC$ . The coefficient of linear expansion of rod is $12\,\,\times\,\,10^{-6}\,/^oC$ . Its Young's modulus of elasticity is $10^{11}\,\,N/m^2$ . The energy stored per unit volume of rod will be  ....... $J/m^3$

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 ........ $J$

  • [AIEEE 2003]

Identical springs of steel and copper are equally stretched. On which more work will have to be done ?

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 $=0.5 \times 10^{9}\, {N} / {m}^{2}$ )

  • [JEE MAIN 2021]