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(D) Let the mass of the moving particle be $m$ and its velocity be $u$. The kinetic energy is $K = \frac{1}{2} m u^2 = 3 \ J$.The mass of the stationa

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All of the above

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(D) Let the mass of the moving particle be $m$ and its velocity be $u$. The kinetic energy is $K = \frac{1}{2} m u^2 = 3 \ J$.The mass of the stationary particle is $2m$. By conservation of linear momentum,the velocity of the center of mass is $v_{cm} = \frac{m u + 2m(0)}{m + 2m} = \frac{u}{3}$.The kinetic energy of the system at the point of maximum compression (when both particles move with $v_{cm}$) is $K_{min} = \frac{1}{2} (m + 2m) v_{cm}^2 = \frac{1}{2} (3m) (\frac{u}{3})^2 = \frac{1}{2} (3m) \frac{u^2}{9} = \frac{1}{3} (\frac{1}{2} m u^2) = \frac{1}{3} (3 \ J) = 1 \ J$.The potential energy stored at maximum compression is $U_{max} = K_{initial} - K_{min} = 3 \ J - 1 \ J = 2 \ J$.Since the kinetic energy decreases from $3 \ J$ to $1 \ J$ and then increases back to $3 \ J$ after the collision,the ratio of kinetic energy to potential energy changes accordingly. Thus,all statements are correct.

$A$ particle with kinetic energy $K = 3 \ J$ makes an elastic head-on collision with a stationary particle of twice its mass. Which of the following statements is correct?

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