Q. A disc and a ring, both of the same mass and radius, are released simultaneously on an inclined plane. Which one will reach the bottom first?

एक डिस्क और एक वलय, दोनों का द्रव्यमान और त्रिज्या समान है, एक झुके हुए तल पर एक साथ छोड़े जाते हैं। कौन सबसे पहले नीचे तक पहुंचेगा?

Ring
चक्राकार

Disc
डिस्क

Both at the same time
दोनों एक ही समय में

Depends on inclination
झुकाव पर निर्भर करता है

Both roll without slipping, so total kinetic energy includes rotational and translational parts. For a rolling object:

\text{Acceleration} \propto \frac{1}{1 + \frac{I}{MR^2}}

For a disc, $I = \frac{1}{2}MR^2$ ;
For a ring, $I = MR^2$ .

Thus, disc has lower moment of inertia relative to mass and radius, so it accelerates faster and reaches the bottom first.

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