A small object of uniform density roll up a curve surface with an initial velocity v.  It reaches up to a maximum height of 3v24g with respect to the initial position. The object is

# A small object of uniform density roll up a curve surface with an initial velocity v.  It reaches up to a maximum height of $\frac{3{v}^{2}}{4g}$ with respect to the initial position. The object is

1. A

Ring

2. B

Solid sphere

3. C

Hollow sphere

4. D

Disc

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### Solution:

$\frac{1}{2}{\mathrm{mv}}^{2}\left(1+\frac{{\mathrm{K}}^{2}}{{\mathrm{R}}^{2}}\right)=\mathrm{mgh}=\mathrm{mg}\frac{3{\mathrm{v}}^{2}}{4\mathrm{g}}$

$\left(1+\frac{{\mathrm{K}}^{2}}{{\mathrm{R}}^{2}}\right)=\frac{3}{2}$

$\frac{{K}^{2}}{{R}^{2}}=\frac{1}{2}$

so it is disc

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