Choose the correct option for the following Assertion (A) and Reason (R).

Question

G1 Physics · Accepted Answer

Let the free-end speed be v. At distance x from the fixed end, v(x) ≈ vx/L. The spring kinetic energy is K = ∫½v(x)² dm. For a uniform spring, dm = (mₛ/L)dx. Therefore, K = ½(mₛ/L) ∫₀ᴸ(v²x²/L²)dx. This gives K = mₛv²/6 = ½(mₛ/3)v². Hence the effective mass is mₛ/3. Both Assertion and Reason are true, and the Reason correctly explains the Assertion. Correct option: A.