A horizontal circular plate rotates with angular speed ω. A person at the centre stretches out two dumbbells, making the system's moment of inertia triple. If initial kinetic energy is E and final kinetic energy is E/x, find x.
Physics · Rotational Motion · angular momentum in pure rotation and its conservation
JEE Mains 11 April 2023 Shift 2 Evening Shift

Question

A horizontal circular plate rotates with angular speed ω. A person at the centre stretches out two dumbbells, making the system's moment of inertia triple. If initial kinetic energy is E and final kinetic energy is E/x, find x.

Physics · Rotational Motion · angular momentum in pure rotation and its conservation

JEE Mains 11 April 2023 Shift 2 Evening Shift

G1 Physics · Accepted Answer

Angular momentum is conserved: Iω = (3I)ω₂, so ω₂ = ω/3. Initial energy E = (1/2)Iω². Final energy E(f) = (1/2)(3I)(ω/3)² = (1/3)(1/2 Iω²) = E/3. Thus x = 3.