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Byju's Answer

Standard XII

Physics

Wedge Problem

A small objec...

Question

A small object of uniform density rolls up a curved surface with an initial velocity $v$ . It reaches up to a maximum height of $\frac{3 v^{2}}{4 g}$ w.r.t. the initial position. The object is a:

ring

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solid sphere

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hollow sphere

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disc

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Solution

The correct option is C disc
By energy balance we get
$\frac{1}{2} m v^{2} + \frac{1}{2} I ω^{2} = m g h$
or
$\frac{1}{2} m v^{2} + \frac{1}{2} I (\frac{v}{R})^{2} = m g \frac{3 v^{2}}{4 g}$
or
$I = \frac{m r^{2}}{2}$
This is the moment of inertia for a solid disc. Thus option D is correct.

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