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Question: Answered & Verified by Expert
A small ring is rolling without slipping on the circumference of a large bowl as shown in the figure. The ring is moving down at $\mathrm{P}_{1}$, comes down to the lower most point $\mathrm{P}_{2}$ and is climbing up at $\mathrm{P}_{3}$. Let $\vec{v}_{C M}$ denote the velocity of the centre of mass of the ring. Choose the correct statement regarding the frictional force on the ring.
PhysicsRotational MotionKVPYKVPY 2017 (19 Nov SB/SX)
Options:
  • A It is opposite to $\overrightarrow{\mathrm{v}}_{\mathrm{CM}}$ at the points $\mathrm{P}_{1}, \mathrm{P}_{2}$ and $\mathrm{P}_{3}$
  • B It is opposite to $\vec{v}_{C M}$ at $P_{1}$ and in the same direction as $\overrightarrow{\mathrm{v}}_{\mathrm{CM}}$ at $\mathrm{P}_{3}$
  • C It is in the same direction as $\vec{v}_{C M}$ at $P_{1}$ and opposite to $\vec{v}_{C M}$ at $P_{3}$
  • D It is zero at the points $\mathrm{P}_{1}, \mathrm{P}_{2}$ and $\mathrm{P}_{3}$
Solution:
1753 Upvotes Verified Answer
The correct answer is: It is opposite to $\vec{v}_{C M}$ at $P_{1}$ and in the same direction as $\overrightarrow{\mathrm{v}}_{\mathrm{CM}}$ at $\mathrm{P}_{3}$
$\mathrm{fr}_{1}$ will increase $\omega$.
$\mathrm{fr}_{3}$ will decrease $\omega$.

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