Question
Two uniform solid spheres having unequal masses and unequal radii are released from rest from the same height on a rough incline. If the spheres roll without slipping,
✓
Answer
(c)
Since acceleration of a body during rolling without slipping, on an inclined plane of angle $\theta$ is given by
$a=\frac{g \sin \theta}{1+\frac{K^2}{R^2}}$, where $K$ is radius of gyration.
For solid sphere, $\frac{ K ^2}{ R ^2}=\frac{2}{5}$
Thus, $a=\frac{5}{7} g \sin \theta$
So, acceleration is independent of both mass and radius. Both spheres will reach bottom together.
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