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6. system of particles and rotational motion — Physics STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 SciencePhysics6. system of particles and rotational motion1 Mark
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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