MCQ
The ratio of the accelerations for a solid sphere (mass $m$ and radius $R$) rolling down an incline of angle $\theta$ without slipping and slipping down the incline without rolling is
- ✓$5:7$
- B$2:3$
- C$2:5$
- D$7:5$
✓
Answer
Correct option: A.
$5:7$
a
Acceleration of the solid sphere slipping down the incline without rolling is
Acceleration of the solid sphere slipping down the incline without rolling is
${a_{slipping}} = g\sin \theta \,\,\,\,\,\,\,...\left( i \right)$
Acceleration of the solid sphere rolling down the incline without slipping is
${a_{rolling}} = \frac{{g\sin \theta }}{{1 + \frac{{{k^2}}}{{{R^2}}}}} = \frac{{g\sin \theta }}{{1 + \frac{2}{5}}}$
$\left( {For\,solid\,sphere,\frac{{{k^2}}}{{{R^2}}} = \frac{2}{5}} \right)$
$= \frac{5}{7}g\sin \theta \,\,\,\,\,...\left( {ii} \right)$
Divide eqn. $(ii)$ by eqn. $(i)$, we get
$\frac{{{a_{rolling}}}}{{{a_{slipping}}}} = \frac{5}{7}$
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