SATHEE: Rotation 3 Question 2

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 $Q$

(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, $a = \frac{g \sin θ}{1 + I / m R^{2}}$

$a_{Q} > a_{P}$ as its moment of inertia is less. Therefore, $Q$ reaches first with more linear speed and more translational kinetic energy.

Further, $ω = \frac{v}{R}$ or $ω \propto v$

$∴ ω_{Q} > ω_{P} as v_{P} > v_{Q}$

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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?

Answer:

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