Two solid cylinders P and Q of same mass and same radius start ro… - Vidyadip

MCQ

Two solid cylinders $P$ and $Q$ of same mass and same radius start rolling down a fixed inclined plane form 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 $Q$ reaches the ground with same translational kinetic energy.
✓
Cylinder $Q$ reaches the ground with larger angular speed.

✓

Answer

Correct option: D.

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

d
$I_p>I_Q $

$a_p=\frac{g \sin \theta}{I_p+m R^2} $

$a_Q=\frac{g \sin \theta}{I_Q+m R^2} $

$a_p < a_Q \Rightarrow v=u+a t \Rightarrow t \propto \frac{1}{a}$

$t_p>t_Q $

$V^2=u^2+2 \text { as } \Rightarrow v \propto a \Rightarrow V_p$

$\text { Translational } K . E .=\frac{1}{2} m V^2 \Rightarrow T R K E_p$

$V=\omega R \Rightarrow \omega \propto V \Rightarrow \omega_p<\omega_Q$

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