Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11
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A Small Disc is Set Rolling with a Speed ν on the Horizontal Part of the Track of the Previous Problem from Right to Left. to What Height Will It Climb up the Curved Part? - Physics


A small disc is set rolling with a speed \[\nu\] on the horizontal part of the track of the previous problem from right to left. To what height will it climb up the curved part?

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Let the radius of the disc be R.

Let the angular velocity of the disc ω.

Let the height attained by the disc be h.

On applying the law of conservation of energy, we get

\[\frac{1}{2}m v^2  + \frac{1}{2}I \omega^2  = mgh\]

\[ \Rightarrow \frac{1}{2}m v^2  + \frac{1}{2} \times \frac{1}{2}m R^2  \times  \left( \frac{v}{R} \right)^2  = mgh\]

\[ \Rightarrow \frac{1}{2} v^2  + \frac{1}{4} v^2  = gh\]

\[ \Rightarrow \frac{3}{4} v^2  = gh\]

\[ \Rightarrow h = \frac{3 v^2}{4g}\]

Concept: Momentum Conservation and Centre of Mass Motion
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HC Verma Class 11, 12 Concepts of Physics 1
Chapter 10 Rotational Mechanics
Q 74 | Page 200
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