A body of mass m₁ = 4 kg moves with velocity 5î m s⁻¹ and another body of mass m₂ = 2 kg moves with velocity 10î m s⁻¹. Find the kinetic energy of their centre of mass in joules.
Physics · Mixed Chapter
JEE Main Practice

Question

A body of mass m₁ = 4 kg moves with velocity 5î m s⁻¹ and another body of mass m₂ = 2 kg moves with velocity 10î m s⁻¹. Find the kinetic energy of their centre of mass in joules.

G1 Physics · Accepted Answer

Step 1: Total mass M = 4 + 2 = 6 kg. Step 2: Total momentum along î: p = m₁v₁ + m₂v₂ = (4 × 5 + 2 × 10)î = 40î kg m s⁻¹. Step 3: Centre-of-mass velocity v⃗₍CM₎ = p⃗/M = (40/6)î = (20/3)î m s⁻¹. Step 4: Translational kinetic energy of centre of mass K₍CM₎ = ½ M |v⃗₍CM₎|² = ½ × 6 × (20/3)² = 400/3 J. Final answer: ≈133.33 J.