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  4. An inclined plane makes an angle of 30° with the horizontal. A solid sphere rolling down this inclined plane from rest without slipping has a linear acceleration equal to

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Q. 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

System of Particles and Rotational Motion

Solution:

$\tau=I \alpha$
$\alpha=\frac{\tau}{I}=\frac{m g r \sin \theta}{\frac{2}{5} m r^{2}+m r^{2}}$
$a=\alpha r=\frac{m g r^{2} \sin \theta}{\frac{2}{5} m r^{2}+m r^{2}}$
$a=\frac{5 g \sin 30^{\circ}}{7}=\frac{5 g}{14}$