A body is rolling down an incline plane. If the rotational K.E. of the body is 40 % of its trans

step 1 is a body is rolling down an incline pain if the rotational kinetic energy of the body is 40 % o

A body is rolling down an incline plane. If the rotational...

A body is rolling down an incline plane. If the rotational $\mathrm{K}$.E. of the body is $40 \%$ of its translational $\mathrm{K} . \mathrm{E}$. then the body is $\ldots$
$\{\mathrm{A}\}$ ring
\{B\} Cylinder
$\{\mathrm{C}\}$ solid sphere
\{D\} hollow sphere

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Key Concepts

Rolling Motion

Rolling motion is the combination of rotational and translational movements, where an object rolls on a surface without slipping. This concept is pivotal in understanding the dynamics of moving bodies on inclined planes and how both forms of kinetic energy come into play.

Kinetic Energy in Rolling Objects

In rolling motion, the total kinetic energy is the sum of translational kinetic energy (energy due to the linear motion of the center of mass) and rotational kinetic energy (energy due to the rotation of the object about its axis). Examining the ratio of these energy components is essential for analyzing the motion of different rolling bodies.

Moment of Inertia

The moment of inertia quantifies how an object's mass is distributed relative to its axis of rotation, affecting its resistance to rotational acceleration. It is a key factor in determining the amount of rotational kinetic energy an object possesses during rolling.

Energy Partitioning in Rolling

Energy partitioning in rolling examines how the total kinetic energy is divided between translational and rotational forms, which depends on the object's moment of inertia. The specific ratio of rotational to translational kinetic energy can be used to differentiate between various shapes, based on their unique inertial properties.

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