Question

If $x$ is ratio of rotational kinetic energy and translatory kinetic energy of rolling body, then which of the following is true ?

• A. $x=1$
• B. $x\le 1$
• C. $x\ge 1$
• D. $x=\frac{1}{2}$

Answer 1

Answer: (B)

$x\le 1$

Rotational kinetic energy= $\frac{1}{2}I{\omega }^2$
Transnational kinetic energy=$\frac{1}{2}m{\nu }^2$
but $V=r\omega$
$\therefore x=\frac{\frac{1}{2}I{\omega }^2}{\frac{1}{2}m{\nu }^2}=\frac{I}{m{r}^2}=K$
Where $K$ is radius of gyration $\le 1$
$\therefore x\le 1$