Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): If a small mass placed on an oscillating horizontal block is suddenly lifted off vertically when the block is exactly at its extreme position, the amplitude of oscillation of the remaining block remains unchanged. Reason (R): At the extreme position, the magnitude of the restoring force acting on t

Step-by-step solution

At the extreme position, the velocity of the oscillating system is zero. When the small mass is lifted off, it takes away zero kinetic energy. The remaining block still has zero kinetic energy and the spring is at the same maximum extension, meaning the potential energy 1 2 kA^2 is unchanged. Since the total mechanical energy of the remaining system is conserved and depends only on the spring constant k and the amplitude, the new amplitude must equal the old amplitude. Thus, Assertion (A) is true. The restoring for