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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
An inclined plane makes an angle of $30^{\circ}$ with the horizontal. A solid sphere rolling down this inclined plane from rest without slipping has a linear acceleration equal to ........
  • A
    $\frac{g}{3}$
  • B
    $\frac{2 g}{3}$
  • C
    $\frac{5 g}{7}$
  • ✓
    $\frac{5 g}{14}$
✓

Answer

Correct option: D.
$\frac{5 g}{14}$
d
(d)

$\tau=I \alpha$

$\alpha=\frac{\tau}{I}=\frac{m g r \sin \theta}{\frac{2}{5} m r^2+m r^2}$

$a=\alpha r=\frac{m g r^2 \sin \theta}{\frac{2}{5} m r^2+m r^2}$

$a=\frac{5 g \sin 30^{\circ}}{7}=\frac{5 g}{14}$

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