Q. 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
A) Both cylinders $P$ and $Q$ reach the ground at the same time
B) Cylinder $P$ has larger linear acceleration than cylinder $Q$
C) Both cylinder $P$ and $Q$ reaches the ground with same translational kinetic energy
D) Cylinder $Q$ reaches the ground with larger angular speed
Explanation
(d) $I_{P} > I_{Q}$
$a_{P} = \frac{g\sin\theta}{I_{P} + mR^{2}}$
$a_{Q} = \frac{g\sin\theta}{I_{Q} + mR^{2}}$
$a_{P} > a_{Q} \Rightarrow V = u + at \Rightarrow t \propto \frac{1}{a}$
$t_{P} > t_{Q}$
$V^{2} = u^{2} + 2as \Rightarrow v \propto a \Rightarrow V_{P} < V_{Q}$
Translational $K.E. = \frac{1}{2}mV^{2} \Rightarrow TR\ KE_{P} < TR\ KE_{Q}$
$V = \omega R \Rightarrow \omega \propto V \Rightarrow \omega_{P} < \omega_{Q}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.