Question

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

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

Answer 1

The correct option is D Cylinder B reaches the ground with larger angular speed

We can treat cylinders A as hollow and B as solid. For hollow cylinder A,
$\frac{K^2}{R^2}=1$ and
Solid Cylinder B, $\frac{K^2}{R^2}=\frac{1}{2}$
$\therefore V_A=\sqrt{\frac{2gh}{1+1}}=\sqrt{2gh}$
$V_B=\sqrt{\frac{2gh}{1+\frac{1}{2}}}=\sqrt{\frac{4gh}{3}}$
$V_B>V_A$
$\therefore {\omega }_B>{\omega }_A$