A solid sphere, a disc and a ring of the same mass and radius are allowed to roll down a frictionless inclined plane simultaneously from the same height. In this context, which one of the following statements is correct?

In classical mechanics, the acceleration of an object rolling down an incline depends on its moment of inertia. However, the question specifies a 'frictionless' inclined plane. For an object to roll without slipping, static friction must be present to provide the necessary torque [t3][t6]. On a frictionless surface, there is no torque to cause rotational acceleration; therefore, the solid sphere, disc, and ring will not roll but will instead slide down the incline [c1][c2]. Since they all start from the same height and experience the same downward acceleration (a = g sinθ) due to gravity without any energy being diverted into rotational kinetic energy, they will all reach the bottom at the same time. If friction were present, the sphere would reach first due to its lower moment of inertia [t2][t7], but in this specific frictionless scenario, they reach simultaneously.

Sources

1. [1] Physical Geography by PMF IAS, Manjunath Thamminidi, PMF IAS (1st ed.) > Chapter 6: Geomorphic Movements > Landslides > p. 89
2. [2] FUNDAMENTALS OF PHYSICAL GEOGRAPHY, Geography Class XI (NCERT 2025 ed.) > Chapter 5: Geomorphic Processes > Landslides > p. 42