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The ratio of the accelerations for a solid sphere (mass ‘ $\mathrm{m}$ ‘ and radius ‘ $\mathrm{R}^{\prime}$ ) rolling down an incline of angle ‘ $\theta$ ‘ without slipping and slipping down the incline without rolling is:Option A $\quad 5: 7$Option B $\quad 2: 3$Option C $\quad 2: 5$Option D $\quad 7: 5$
The ratio of the accelerations for a solid sphere (mass ‘ $\mathrm{m}$ ‘ and radius ‘ $\mathrm{R}^{\prime}$ ) rolling down an incline of angle ‘ $\theta$ ‘ without slipping and slipping down the incline without rolling is:
Option A $\quad 5: 7$
Option B $\quad 2: 3$
Option C $\quad 2: 5$
Option D $\quad 7: 5$
Physics
The ratio of the accelerations for a solid sphere (mass ‘ $\mathrm{m}$ ‘ and radius ‘ $\mathrm{R}^{\prime}$ ) rolling down an incline of angle ‘ $\theta$ ‘ without slipping and slipping down the incline without rolling is:
Option A $\quad 5: 7$
Option B $\quad 2: 3$
Option C $\quad 2: 5$
Option D $\quad 7: 5$

The correct option is A

For rolling motion without slipping on inclined plane acceleration is given by

$a_{\text {rolling }}=\frac{g \sin \theta}{1+\frac{K^{2}}{R^{2}}}=\frac{g \sin \theta}{1+\frac{2}{5}}$

For solid sphere we can write, $\left(\frac{\mathrm{k}^{2}}{\mathrm{R}^{2}}=\frac{2}{5}\right)$

And for slipping motion on inclined plane $\mathrm{a}_{\text {slipping }}=\mathrm{g} \operatorname{Sin} \theta$

Required ratio $=\frac{a_{\text {rolling }}}{a_{\text {slipping }}}=\frac{1}{1+\frac{2}{5}}=\frac{5}{7}$

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