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Physics · WORK, ENERGY AND POWER
हिन्दीThe figure illustrates the plots of potential energy \( V(x) \), kinetic energy \( K(x) \), and total mechanical energy \( E \) for a block attached to an ideal linear spring obeying Hooke's law. At what value of displacement \( x \) do the potential energy and kinetic energy curves intersect?
Correct answer · Option 3
\( x = \pm \frac{x_m}{\sqrt{2}} \)
Explanation
At the intersection, \( V(x) = K(x) = \frac{E}{2} \). Since \( V(x) = \frac{1}{2}kx^2 \) and \( E = \frac{1}{2}kx_m^2 \), we have \( \frac{1}{2}kx^2 = \frac{1}{2}(\frac{1}{2}kx_m^2) \implies x^2 = \frac{x_m^2}{2} \implies x = \pm \frac{x_m}{\sqrt{2}} \).
