Question

A block 'A' of mass$m_1$ hits horizontally the rear side of a spring (ideal) attached to a block B of mass $m_2$ resting on a smooth horizontal surface. After hitting, 'A' gets attached to the spring.
Some statements are given at any moment of time:
i. If velocity of A is greater than B, then kinetic energy of the system will be decreasing.
ii. If velocity of A is greater than B, then kinetic energy of the system will be increasing.
iii. If velocity of A is greater than B, then momentum of the system will be decreasing.
iv. If velocity of A is greater than B, then momentum of the system will be increasing.
Now select correct alternative

• A. only iv
• B. only i
• C. ii and iv
• D. i and iii

Answer 1

The correct option is B only i

Just after collision, the speed of A will keep on decreasing and that of B will keep on increasing untill both attain a common speed. At this point, the spring is compressed to the maximum and the initial kinetic energy of A is now the sum of kinetic and potential energies of the system. At this point, potential energy is maximum and kinetic energy is minimum. So, till this point after collision, the kinetic energy decreases and potential energy increases. After this point, there will be oscillation between kinetic and potential energies because the spring is linear. But the total momentum is always the same because momentum is conserved. On an average, it can be said that the kinetic energy of the system decreases because a part of it is converted to the potential energy of the spring.