Two objects, X and Y, are held at rest on a horizontal frictionless surface and a spring is compressed between them.The mass of X is 2/5 times the mass of Y.Immediately after the spring is released, X has a kinetic energy of 50 J and Y has a kinetic energy of:
A)20 J
B)8 J
C)310 J
D)125 J
E)50 J

Question

Quizplus · Accepted Answer

Since the surface is frictionless and the system is isolated, the principle of conservation of mechanical energy applies. The total energy in the system before and after the spring is released remains constant. When the spring is released, its potential energy is converted into the kinetic energy of objects X and Y. Because momentum is conserved and the system is initially at rest, the velocities of X and Y are inversely proportional to their masses. Given that the mass of X is 2/5 times the mass of Y, and X has a kinetic energy of 50 J, the kinetic energy of Y must be less due to its greater mass. The kinetic energy ratio between two objects in such a scenario is inversely proportional to the ratio of their masses, making the correct answer 20 J, as it reflects the appropriate distribution of energy based on their mass ratio and the conservation of energy principle.

Two Objects, X and Y, Are Held at Rest on a Horizontal