Physics - SHM Question with Solution | TestHub
A block with mass M is connected by a massless spring with stiffness constant k to a rigid wall and moves without friction on a horizontal surface. The block oscillates with small amplitude A about an equilibrium position . Consider two cases : (i) when the block is at ; and (ii) when the block is at . In both the cases, a particle with mass m (<M) is softly placed on the block after which they stick to each other. Which of the following statement(s) is(are) true about the motion after the mass m is placed on the mass M?
Options:(select one or more)
Answer:
Solution:
Case I (mass added at x₀): momentum conservationso the velocity at equilibrium position decreases.
By energy conservation,
Case II (mass added at x₀ + A): the block is instantaneously at rest, so there is no energy loss and the amplitude remains the same.
In both cases ω decreases, so the speed at x₀ decreases in both cases.
The final time periodis the same in both cases.
Hence (A), (B), (D) are correct; energy decreases only in case I, so (C) is wrong.
