Question

Two solid cylinders $P$ and $Q$ of same mass and same radius start rolling down a fixed inclined plane from the same height at the same time. Cylinder $P$ has most of its mass concentrated near its surface, while $Q$ has most of its mass concentrated near the axis. Which statement(s) is (are) correct ?

• A. Both cylinders $P$ and $Q$ reach the ground at the same time.
• B. Cylinder $P$ has larger linear acceleration than cylinder $Q$.
• C. Both cylinders reach the ground with same translational kinetic energy.
• D. Cylinder $Q$ reaches the ground with larger angular speed.

Answer 1

The correct option is D Cylinder $Q$ reaches the ground with larger angular speed.

Acceleration is
$a=\frac{MGsin\theta }{M+\frac{I}{R^2}}$
$a_P=\frac{MGsin\theta }{M+\frac{M{R}^2}{R^2}}=\frac{g}{2}$
$a_Q=gsin\theta$ as $i_Q$ is similar to $0$
${\omega }_p=\frac{\sqrt{2\ast \frac{g}{2}l}}{R}$

${\omega }_Q=\frac{\sqrt{2gl}}{R}$ Thus ${\omega }_p>{\omega }_Q$