Question

In figure $E$ and $V_{cm}$ represent the total energy and speed of centre of mass of an object of mass $1kg$ in pure rolling. The object is:

• A. Sphere
• B. Ring
• C. Disc
• D. Hollow Cylinder

Answer 1

Answer: (C)

$E=\frac{1}{2}m{v}_{cm}^2\left[1+\frac{K^2}{R^2}\right]$
$\frac{E}{v_{cm}^2}=\frac{1}{2}\left[1+\frac{K^2}{R^2}\right]$
From graph, $\frac{E}{v_{cm}^2}=\frac{3}{4}$
$\frac{3}{4}=\frac{1}{2}\left[1+\frac{K^2}{R^2}\right]$
$\frac{3}{2}-1=\frac{K^2}{R^2}$
$\frac{K^2}{R^2}=\frac{1}{2}$
For disc, $I=\frac{m{R}^2}{2}$
$\frac{m{R}^2}{2}=m{K}^2$
$\frac{K^2}{R^2}=\frac{1}{2}$