A particle of mass m moving horizontally at speed u sticks to an equal mass m initially resting at the end of a pendulum string of length 2ℓ. The string then swings 60° before stopping. If u=√(xgℓ), find x.
Physics · Mixed Chapter
JEE Main Practice

Question

A particle of mass m moving horizontally at speed u sticks to an equal mass m initially resting at the end of a pendulum string of length 2ℓ. The string then swings 60° before stopping. If u=√(xgℓ), find x.

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1: Horizontal momentum at sticking collision gives mu=(2m)v ⇒v=u/2. Step 2: The combined mass rises Δh=2ℓ(1−cos60°)=ℓ. Step 3: Mechanical energy after impact: ½(2m)(u/2)²=(2m)gℓ. Step 4: mu²/4=2mgℓ ⇒u²=8gℓ; x=8.