Answer:
Both have the same acceleration.
Explanation:
Energy is conserved. The initial potential energy at the top of the incline = the final translational kinetic energy at the bottom + the rotational energy.
PE = KE + RE
mgh = ½ mv² + ½ Iω²
For a sphere, I = ⅖ mr². For rolling without slipping, ω = v/r.
mgh = ½ mv² + ½ (⅖ mr²) (v/r)²
mgh = ½ mv² + ⅕ mv²
gh = ½ v² + ⅕ v²
gh = ⁷/₁₀ v²
v² = ¹⁰/₇ gh
The final velocity is independent of the mass or radius. So two balls that roll down an incline from the same height will have the same velocity at the bottom, and therefore the same acceleration.
