Two solid cylinders P and Q of same mass and same radius start...

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 of its mass concentrated near the axis. Which statement(s) is(are) correct? Two solid cylinders P and Q of same mass and same radius start rolling down a fixed inclined plane from the same height

Two solid cylinders P and Q of same mass and same radius start rolling down a fixed inclined plane from the same height

Options

ABoth cylinders $P$ and $Q$ reach the ground at the same time.
BCylinders $P$ has larger linear acceleration than cylinder $Q$ .
CBoth cylinders reach the ground with same translational kinetic energy.
DCylinder $Q$ reaches the ground with larger angular speed.

Correct answer

D. Cylinder $Q$ reaches the ground with larger angular speed.

Step-by-step solution

As we know, acceleration of the center of mass of cylinder rolling down an inclined plane

a_{c}=\frac{g \sin \theta}{1+\frac{I}{M R^{2}}}

In case of

P

the mass is concentrated away from the axis, So

I_{P}>I_{Q}

\therefore \quad a_{P} < a_{Q} \Rightarrow v_{\mathrm{P}} < v_{\mathrm{Q}} \Rightarrow \omega_{\mathrm{P}} < \omega_{\mathrm{Q}}

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