A solid sphere rolls without slipping. If Kₜ is its translational kinetic energy and Kᵣ its rotational kinetic energy, find Kₜ:(Kₜ+Kᵣ).
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A solid sphere rolls without slipping. If Kₜ is its translational kinetic energy and Kᵣ its rotational kinetic energy, find Kₜ:(Kₜ+Kᵣ).

G1 Physics · Accepted Answer

Step 1: Kₜ=½Mv². Step 2: For a solid sphere I=2MR²/5 and ω=v/R, giving Kᵣ=½(2/5MR²)(v²/R²)=Mv²/5. Step 3: Thus Kₜ/(Kₜ+Kᵣ)=(1/2)/(1/2+1/5)=5/7. Final answer: B — 5:7.