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Physics · WORK, ENERGY AND POWER
हिन्दीA block of mass \( m \) is attached to a spring of force constant \( k \) and executes horizontal oscillations with maximum amplitude \( x_m \). The speed of the block at a position where its kinetic energy is equal to three times its potential energy is:
Correct answer · Option 4
\( \frac{\sqrt{3}}{2} \sqrt{\frac{k}{m}} x_m \)
Explanation
Total energy \( E = \frac{1}{2}k x_m^2 = K + V \). Given \( K = 3V \implies V = \frac{1}{4}E \), so \( K = \frac{3}{4}E \). Thus, \( \frac{1}{2}m v^2 = \frac{3}{4}(\frac{1}{2}k x_m^2) \implies v = \frac{\sqrt{3}}{2} \sqrt{\frac{k}{m}} x_m \).
