A solid sphere and a hollow sphere roll without slipping from rest through equal distances on the same inclined plane. If their times are t₁ and t₂ respectively, then:
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A solid sphere and a hollow sphere roll without slipping from rest through equal distances on the same inclined plane. If their times are t₁ and t₂ respectively, then:

G1 Physics · Accepted Answer

For pure rolling, a=g sinθ/[1+I/(mR²)]. For a solid sphere I=2mR²/5, so a S S = 5 g a_SS=5g a S ​ S = 5 g sinθ/7. For a hollow sphere I=2mR²/3, so a H S = 3 g a_HS=3g a H ​ S = 3 g sinθ/5. Hence a S S > a H S . a_SS>a_HS. a S ​ S > a H ​ S . For the same distance from rest, t∝1/√a, therefore t₁<t₂.