A body of mass 5 kg is whirled in a vertical circle by a string 1 m long. Calculate the velocity at the top of the circle for just completing the vertical loop (m s⁻¹).
Physics · Mixed Chapter
JEE Main Practice

Question

A body of mass 5 kg is whirled in a vertical circle by a string 1 m long. Calculate the velocity at the top of the circle for just completing the vertical loop (m s⁻¹).

G1 Physics · Accepted Answer

Step 1: For just completing a vertical loop, the string tension at the top approaches zero. Step 2: Radial force at top: mg + T = mv²/r. At the limiting case T = 0. Step 3: Therefore vₜ² = gr and vₜ = √(gr). Step 4: With r = 1 m and g ≈ 9.8 m s⁻², vₜ = √9.8 ≈ 3.13 m s⁻¹. Final answer to one decimal place: 3.1 m s⁻¹.