A solid cylinder and a hollow cylinder both of the same mass and same external diameter are released from…
A solid cylinder and a hollow cylinder both of the same mass and same external diameter are released from the same height at the same time on an inclined plane. Both roll down without slipping. Which one will reach the bottom first?
Solid cylinder
Both together
One with higher density
Hollow cylinder
Solution
Solid cylinder reaches the bottom first because for solid cylinder $\frac{\mathrm{K}^{2}}{\mathrm{R}^{2}}=\frac{1}{2}$ and for hollow cylinder, $\frac{\mathrm{K}^{2}}{\mathrm{R}^{2}}=1$.
Acceleration down the inclined plane $\propto \frac{1}{1+K^{2} / R^{2}} .$ Solid cylinder has greater acceleration. It reaches the bottom first.