Q108 / 125 · BITSAT 2020 · Physics
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?
- Correct answerASolid cylinder
- BBoth together
- COne with higher density
- DHollow 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.
Hence, the correct answer is option: 'A'.