NEETPhysicsOscillations
Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): When two different masses m₁ and m₂ ( m₁ > m₂ ) attached to identical springs oscillate with the same amplitude, the lighter mass m₂ will possess a greater maximum kinetic energy. Reason (R): The maximum kinetic energy of a spring-mass system depends only on the spring constant and the amplitude, a
Options
- ABoth (A) and (R) are correct and (R) is the correct explanation of (A)
- BBoth (A) and (R) are correct but (R) is not the correct explanation of (A)
- C(A) is correct but (R) is not correct
- D(A) is not correct but (R) is correct
Correct answer
D. (A) is not correct but (R) is correct
Step-by-step solution
The maximum kinetic energy of a spring-mass system is given by K_ = 1 2 m v_ ^2 . Since v_ = A and = k m , substituting these gives: K_ = 1 2 m (A k m )^2 = 1 2 k A^2 . This shows that the maximum kinetic energy depends only on the spring constant k and the amplitude A . It is completely independent of the mass m . Therefore, the Reason (R) is correct. Because both masses are attached to identical springs (same k ) and oscillate with the same amplitude (same A ), they will have exactly the same maximum kinetic ener