Question

Two uniform solid spheres having unequal masses and unequal radii are released from rest from the same height on a rough incline. The spheres roll without slipping. Then:

• A. Heavier sphere reaches the bottom first
• B. Bigger sphere reaches the bottom first
• C. Both spheres reach the bottom together
• D. The information given is not suffficient to decide which reaches the bottom first

Answer 1

The correct option is C Both spheres reach the bottom together

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.