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 $$\dfrac{3v^2}{4g}$$ w.r.t. the initial position. The object is a:

A
ring
B
solid sphere
C
hollow sphere
D
disc

Solution

## The correct option is C discBy energy balance we get$$\displaystyle\frac{1}{2}mv^2 + \displaystyle\frac{1}{2}I\omega^2=mgh$$or$$\displaystyle\frac{1}{2}mv^2+\displaystyle\frac{1}{2}I(\displaystyle\frac{v}{R})^2=mg\displaystyle\frac{3v^2}{4g}$$or$$I=\displaystyle\frac{mr^2}{2}$$This is the moment of inertia for a solid disc. Thus option D is correct.Physics

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