Two equal masses m are connected by a taut string and constrained to a frictionless vertical circular ring of radius R. At release, one is at the top and the other at the leftmost point (chord at 45°). The string tension is mg/√x. Find x.
Physics · Mixed Chapter
JEE Main Practice

Question

Two equal masses m are connected by a taut string and constrained to a frictionless vertical circular ring of radius R. At release, one is at the top and the other at the leftmost point (chord at 45°). The string tension is mg/√x. Find x.

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1: Tension acts along the chord connecting the top and leftmost points. Step 2: Tangential forces include the gravity component on the left mass and equal/opposite projections of tension on both beads. Step 3: Applying the common string-length constraint to the tangential accelerations at release gives T = mg/√2. Step 4: Comparison with mg/√x yields x = 2.