A solid sphere and solid cylinder of identical radii approach an … - Vidyadip

MCQ

A solid sphere and solid cylinder of identical radii approach an incline with the same linear velocity (see figure). Both roll without slipping all throughout. The two climb maximum heights $h_{sph}$ and $h_{cyl}$ on the incline. The radio $\frac{{{h_{sph}}}}{{{h_{cyl}}}}$ is given by

A
$1$
B
$\frac{4}{5}$
C
$\frac{2}{{\sqrt 5 }}$
✓
$\frac{14}{15}$

✓

Answer

Correct option: D.

$\frac{14}{15}$

d
For solid sphere

$\frac{1}{2}m{v^2} + \frac{1}{2} \cdot \frac{1}{2}m{R^2} \cdot \frac{{{V^2}}}{{{R^2}}} = mg{h_{sph}}$

For solid cylinder

$\frac{1}{2}m{V^2} + \frac{1}{2} \cdot \frac{1}{2}m{R^2} \cdot \frac{{{V^2}}}{{{R^2}}} = mg{h_{cyl}}$

$ \Rightarrow \frac{{{h_{sph}}}}{{{h_{cyl}}}} = \frac{{7/5}}{{3/2}} = \frac{{14}}{{15}}$

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