Question

Two solid discs of radii $r$ and $2r$ roll from the top of an inclined plane without slipping. Then

• A. The bigger disc will reach the horizontal level first
• B. The smaller disc will reach the horizontal level first
• C. The time difference of reaching of the discs at the horizontal level will depend on the inclination of the plane
• D. Both the discs will reach at the same time

Answer 1

The correct option is D Both the discs will reach at the same time

$I=m{k}^2=\frac{m{R}^2}{2}$
$implies\frac{k^2}{R^2}=\frac{1}{2}$
As acceleration $a=\frac{g\sin \theta }{(1+\frac{k^2}{R^2})}$
$\Rightarrow a=\frac{g\sin \theta }{(1+\frac{1}{2})}=\frac{2g\sin \theta }{3}$
It is independent of the radius for the same shape.
Thus both will have same acceleration and thus reach the bottom at the same time.