Question

An inclined plane makes an angle 30° with the horizontal. A solid sphere rolling down an inclined plane from rest without slipping has linear acceleration ______. (g = acceleration due gravity) (sin 30° = 0.5)

Options

• \[\frac {5g}{7}\]

• \[\frac {5g}{14}\]

• \[\frac {2g}{3}\]

• \[\frac {g}{3}\]

Answer 1

An inclined plane makes an angle 30° with the horizontal. A solid sphere rolling down an inclined plane from rest without slipping has linear acceleration \[\frac {5g}{14}\].

Explanation:

a = \[\frac{\mathrm{g}\sin\theta}{\left(1+\frac{\mathrm{K}^2}{\mathrm{R}^2}\right)}=\frac{\mathrm{g}\sin30^\circ}{\left(1+\frac{2}{5}\right)}\]

\[\therefore\] a = \[\frac {5g}{7}\] × 0.5 = \[\frac {5g}{14}\]