Question

A hollow cylinder and a solid cylinder of the same mass and radius are released simulta-neously from rest at the top of the same inclined plane. Which will reach the ground first?

• A. Solid cylinder
• B. Hollow cylinder
• C. Both will reach at the same time
• D. Cannot be predicted

Answer 1

Answer: (A)

The acceleration of a body down an incline is given by $a=\frac{g\sin \theta }{1+\frac{K^2}{R^2}}$
where $K$ is radius of gyration, $R$ the radius of the body.
For a hollow cylinder moment of inertia $I$ is $I=M{R}^2$
For a solid cylinder $I=M{\left(\frac{R}{\sqrt{2}}\right)}^2$
Also, $I=M{K}^2\therefore K_{\text{solid }}<K_{\text{hollow }}$
$\Rightarrow$ acceleration ${}_{\text{Solid }}>$ acceleration ${}_{\text{hollow }}$
Hence, solid cylinder will reach first.