The elastic energy stored in a wire of Young's modulus $Y$ is
$Y \times \frac{{{\rm{Strai}}{{\rm{n}}^{\rm{2}}}}}{{{\rm{Volume}}}}$
Stress $ \times $ Strain $ \times $ Volume
$\frac{{{\rm{Stres}}{{\rm{s}}^{\rm{2}}} \times {\rm{Volume}}}}{{2Y}}$
$\frac{1}{2}Y \times $ Stress $ \times $ Strain $ \times $ Volume
The area of cross-section of a railway track is $0.01\, {m}^{2}$. The temperature variation is $10^{\circ} {C}$. Coefficient of linear expansion of material of track is $10^{-5} /{ }^{\circ} {C}$. The energy stored per meter in the track is ...... ${J} / {m} .$
(Young's modulus of material of track is $10^{11} \,{Nm}^{-2}$ ))
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
An aluminium rod with Young's modulus $Y =7.0$ $\times 10^{10} N / m ^2$ undergoes elastic strain of $0.04 \%$. The energy per unit volume stored in the rod in SI unit is:
$K$ is the force constant of a spring. The work done in increasing its extension from ${l_1}$ to ${l_2}$ will be
If the tension on a wire is removed at once, then