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.