Rotation 3 Question 2
8. 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?
(2012)
(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 cylinders reach the ground with same translational kinetic energy
(d) Cylinder $Q$ reaches the ground with larger angular speed
Show Answer
Answer:
Correct Answer: 8. (d)
Solution:
- $I _P>I _Q$
In case of pure rolling, $\quad a=\frac{g \sin \theta}{1+I / m R^{2}}$
$a _Q>a _P$ as its moment of inertia is less. Therefore, $Q$ reaches first with more linear speed and more translational kinetic energy.
Further, $\quad \omega=\frac{v}{R}$ or $\omega \propto v$
$$ \therefore \quad \omega _Q>\omega _P \text { as } v _P>v _Q $$
