Question

A solid sphere, a hollow sphere and a disc, all having same mass and radius, are placed at the top of an incline and released. The friction coefficients between the objects and the inclined plane are same but not sufficient to allow pure rolling. The time taken to reach bottom will be least for

• A. Solid sphere
• B. Hollow sphere
• C. Disc
• D. All of the above reach ground at same time

Answer 1

The correct option is D All of the above reach ground at same time


Since linear acceleration is the same for all i.e.
$a=g\sin \theta -\mu g\cos \theta$
As they have the same mass $\left(m\right)$ and friction coefficient $\left(\mu \right)$
Distance covered, $s=\frac{1}{2}a{t}^2$
Since all three starts from rest and cover equal distance while accelerating at same rate, we can conclude that all will reach the bottom simultaneously.
Hence option (d) is correct