First slide

Rolling motion

Question

A solid sphere rolls down without slipping from rest on a $30^{0}$ incline. Its linear acceleration is

Easy

A

5g/7
B

5g/14
C

2g/3
D

g/3

Solution

For solid sphere $\large \frac{{{k^2}}}{{{R^2}}} = \frac{2}{5},\theta = {30^0}$
Here k = radius of gyration = I_c/m
$\large a = \frac{{g\sin \theta }}{{1 + \frac{{{k^2}}}{{{R^2}}}}} = \frac{{g \times \frac{1}{2}}}{{1 + \frac{2}{5}}} = \frac{{5g}}{{14}}$

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