A hollow sphere is rolling on a plane surface about its axis of symmetry. The ratio of rotational kinetic energy to its total kinetic energy is x/5. The value of x i s ________.

Question

G1 Physics · Accepted Answer

For a hollow sphere: I = (2/3)mR² For rolling without slipping: v = ωR Rotational kinetic energy: K(rot) = ½Iω² = ½ × (2/3)mR²ω² = (1/3)mR²ω² Translational kinetic energy: K(trans) = ½mv² = ½mR²ω² Total kinetic energy: K(total) = (1/3 + 1/2)mR²ω² = (5/6)mR²ω² Therefore: K(rot)/K(total) = (1/3)/(5/6) = 2/5 Hence: x = 2