First slide

Rolling motion

Question

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

Moderate

A

g /3
B

2g/3
C

5g/7
D

5g/14

Solution

$\begin{array}{l} a = \frac{M}{{(M + \frac{I_{cm}}{R^{2}})}^{\times}} \times \sin θ \\ = \frac{M}{(M + \frac{2}{5} \frac{{MR}^{2}}{R^{2}})} \times gsin 30 = \frac{5 g}{14} \end{array}$

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