A solid uniform sphere and a thin uniform hollow spherical shell have equal masses and equal radii. Both are released from rest, from the same…

Write the rolling condition with $I=kmR^2$: $a=\dfrac{g\sin\theta}{1+k}$, friction $f=\dfrac{k}{1+k}mg\sin\theta$ and $v^2=\dfrac{2gh}{1+k}$. For the solid sphere $k=2/5$, giving $a=\tfrac57 g\sin\theta$ and $f=\tfrac27 mg\sin\theta$. For the shell $k=2/3$, giving $a=\tfrac35 g\sin\theta$ and $f=\tfrac25 mg\sin\theta$. (A) is false because $v^2=\tfrac{10}{7}gh$ for the sphere but $\tfrac65 gh$ for the shell. (B) is true: the sphere has the larger acceleration over the same distance, so it takes less time. (C) is true since $\tfrac25>\tfrac27$. (D) is false: the requirement is $\mu\ge \dfrac{k}{1+k}\tan\theta$, which is larger for the shell, not the sphere.