Question

A disk and a solid sphere of same radius but different masses roll off on two inclined planes of the same altitude and length. Which one of the two objects gets to the bottom of the plane first?

• A. Both reach at the same
• B. Disk
• C. Sphere
• D. Depends on their masses

Answer 1

The correct option is C Sphere

Time taken to reach the bottom of inclined plane

$t=\sqrt{\frac{2l(1+\frac{k^2}{R^2})}{g\sin \theta }}$

$\text{For disc}=\frac{k^2}{R^2}=\frac{1}{2}$
$\text{For sphere}=\frac{k^2}{R^2}=\frac{2}{5}$
$\text{For solid sphere}=\frac{k^2}{R^2}\downarrow \text{so t}\downarrow$

Hence, option (b) is the correct answer.