Question

A solid sphere and a solid cylinder having the same mass and radius, roll down the same incline. What will the ratio of their acceleration be?

Answer 1

acceleration, $a\propto \frac{1}{MoI}=\frac{1}{I}$

For cylinder, $I_c=\frac{1}{2}{mr}^2$

For sphere, $I_s=\frac{2}{3}{mr}^2$

$\therefore \frac{a_c}{a_s}=\frac{I_s}{I_c}=\frac{\frac{2}{3}{mr}^2}{\frac{1}{2}{mr}^2}=\frac{2}{3}\times 2=\frac{4}{3}$