A moving m–spring–2m system has initial common speed v, with unstrained spring K. Mass 2m collides perfectly inelastically with stationary mass m. If maximum spring compression is √(mv²/(nk)), find n/2. [See Image.]
Physics · Mixed Chapter
JEE Main Practice

Question

A moving m–spring–2m system has initial common speed v, with unstrained spring K. Mass 2m collides perfectly inelastically with stationary mass m. If maximum spring compression is √(mv²/(nk)), find n/2. [See Image.]

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1 — Before collision the spring is at natural length and both moving blocks travel at v. Inelastic collision of 2m with stationary m gives combined velocity v′=(2m v)/(3m)=2v/3. Step 2 — Two spring-connected masses after impact are m and 3m. Reduced mass μ = m(3m)/(m+3m)=3m/4. Step 3 — Initial relative speed is v−2v/3=v/3. At maximum spring compression the relative speed is zero. Step 4 — (1/2)μ(v/3)²=(1/2)kx² ⇒ x²=(3m/4)(v²/9)/k = mv²/(12k). Step 5 — Source form x=√(mv²/(nk)) gives n=12,…