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 tome
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 angualr speed.

Answer

D

Explanation

As is know from theory, acceleration of a mass rolling down a fixed inclined plane of inclination `theta` is
`a = (g sin theta)/(1+K^(2)//R^(2)` ..(i)
As cylinder `P` has most of its mass concentrated near its surface, while cylinder `Q` has most of its mass concentrated near teh axis, therefore, radius of gyration, `K_(P) gt K_(Q)`
From (i), `a_(P) gt a_(Q)`
Therefore, at bottom of incline, `V_(P) lt V_(Q)`
or `(omega_(P)R) lt (omega_(Q) R) or omega_(P) lt omega_(Q) or omega_(Q) gt omega_(P)` i.e. cylinder `Q` reaches the ground with larger angular speed. Choice (d) is correct.