Two blocks A and B of mass m and 2m respectively are connected by a massless spring of spring constant K. This system lies over a smooth horizontal surface. At t = 0 the block A has velocity u towards right as shown while the speed of block B is zero, and the length of spring is equal to its natural length at that instant. In each situation of column-I, certain statements are given and corresponding results are given in column-II, Match the statements in column-I to the corresponding results in column-II:
Column-I | Column-II |
(i) The velocity of block A | [A] Can never be zero |
(ii) The velocity of block B | [B] may be zero at certain instants of time |
(iii) The kinetic energy of system of two blocks | [C] is minimum at maximum compression of spring |
(iv) The potential energy of spring | [D] is minimum at maximum extension of spring |
Text Solution
Verified by ExpertsA
1. Velocity of Block A:
- Block A started with an initial velocity 'u' and there are no external forces acting on it. The mass of block A is not sufficient for it to ever come to rest since momentum must be conserved in this closed system.
- Hence, its velocity can never be zero, matching it with [A].
2. Velocity of Block B:
- Initially, block B is at rest. As block A moves towards the right, it will compress the spring and transfer momentum to block B. However, depending on the compression and subsequent extension of the spring, there can be moments where block B's velocity can be zero, matching it with [B].
3. Kinetic Energy of the System:
- The system has maximum kinetic energy when the spring is neither stretched nor compressed. At maximum compression, both blocks momentarily stop, resulting in minimum kinetic energy, matching it with [C].
4. Potential Energy of the Spring:
- The potential energy in the spring is zero when the spring is at its natural length. When the spring is at maximum extension, it holds maximum potential energy, meaning it’s minimum when stretched or compressed optimally. Thus, it matches with [D].
Final Matching:
(i) → [A]
(ii) → [B]
(iii) → [C]
(iv) → [D]
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