Question

A body is rolling without slipping on a horizontal floor. The translation kinetic energy is $\frac{2}{3}rd$ of the total kinetic energy. Identify the body

• A. Hollow Cylinder
• B. Hollow Sphere
• C. Solid Sphere
• D. Solid Cylinder

Answer 1

The correct option is D Solid Cylinder

$(K.E{)}_R+(K.E{)}_T=K.E$

or,

$(K.E{)}_R=(K.E)-\frac{2}{3}(K.E)$
or,

$(K.E{)}_R=\frac{1}{3}(K.E)$
$\therefore \frac{(K.E{)}_R}{(K.E{)}_T}=\frac{(\frac{1}{3}K.E)}{(\frac{2}{3}K.E)}=\frac{1}{2}$

or,

$\frac{\frac{1}{2}I{\omega }^2}{\frac{1}{2}M{v}^2}=\frac{1}{2}$

or,

$\frac{\frac{1}{2}I\left(v^2/R^2\right)}{\frac{1}{2}M{v}^2}=\frac{1}{2}$ $(\because \omega =\frac{v}{R})$

or,

$I=\frac{1}{2}M{R}^2$
It is the Moment of Inertia of the solid cylinder about its axis.

(option D)