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 its mass concentrated near the axis. Which statement(s) is (are) correct?

Options

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

Answer

D

Explanation

The acceleration of a body rolling down a smooth inclined plane of inclination `theta` is given by
`a=(g sin theta)/(1+(K^(2))/(r^(2))) " "` ….(1)
Cylinder P acts like a hollow cylinder as most of its mass is concentrated near its surface while for cylinder Q, most of its mass is concentrated near its axis.
`therefore I_(P)gt I_(Q)` or `K_(P)^(2)gt K_(Q)^(2)` (as both have the same mass)
`therefore` from (1), `a_(P)lt a_(Q)` or `a_(Q)gt Q_(P)`
When they reach the bottom, `V_(Q)gt V_(P)`. Hence they will have different kinetic energies but `v = R omega`.
As `omega_(Q)R gt omega_(Q)P` or `omega_(Q)gt omega_(P)`
`therefore` Cylinder Q reaches the ground with larger angular speed and thus (d) is the correct option.