In the case of falling, rolling and sliding from same height...

In the case of falling, rolling and sliding from same height :
(a) the falling body reaches bottom first and rolling at last
(b) the acceleration is maximum in falling and minimum in rolling
(c) the velocity of sliding is greater than that of rolling
(d) all the above

Key Concepts

Free Fall Dynamics

Free fall refers to the motion of an object experiencing gravitational acceleration with no other forces acting significantly on it. In this scenario, all the gravitational potential energy is converted into translational kinetic energy, resulting in the highest possible acceleration and velocity over a given distance.

Sliding Motion

Sliding motion, often considered on an ideally frictionless inclined plane, involves an object moving by converting its gravitational potential energy entirely into translational kinetic energy. Consequently, the object achieves a greater velocity compared to a rolling object where energy is shared between translational and rotational motion.

Rolling Motion

Rolling motion is characterized by an object both translating and rotating as it moves down an incline. Because part of the gravitational potential energy converts into rotational kinetic energy, the translational speed (and thus acceleration) is lower compared to both free falling and sliding objects, meaning it reaches the bottom last of the three cases.

Conservation of Energy

The principle of conservation of energy underpins the analysis of free fall, sliding, and rolling. It states that the gravitational potential energy lost by the object is converted into kinetic energy. In free fall and sliding, the energy transitions wholly into translational kinetic energy, while in rolling motion, a portion of the energy is diverted into rotational kinetic energy, affecting the overall speed and acceleration.

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