• # question_answer A particle moves in a straight line with retardation proportional to its is placement. Its loss of kinetic energy for any displacement $x$ is proportional to A) ${{x}^{2}}$                                   B) ${{e}^{x}}$           C)   $x$                 D)   ${{\log }_{e}}x$

The given condition is that of simple harmonic motion. As the particle moves from mean position to any other position, its potential energy increases by $\frac{1}{2}K{{x}^{2}},$ so in conformance with mechanical  energy conservation its kinetic energy must decrease by $\frac{1}{2}K{{x}^{2}}.$ Hence, the correction option is (a).