Question

A hollow spherical ball of radius $2\text{m}$ and mass $3\text{kg}$ is rotating about a fixed axis passing through its COM. If it has kinetic energy of $576\text{J}$, the angular speed of the hollow spherical ball about the fixed axis is

• A. $12\text{rad/s}$
• B. $9.8\text{rad/s}$
• C. $6\text{rad/s}$
• D. $15.5\text{rad/s}$

Answer 1

The correct option is A $12\text{rad/s}$

Given,
Radius of hollow sphere $\left(r\right)=2\text{m}$
Mass of hollow sphere $\left(m\right)=3\text{kg}$
Kinetic energy of hollow sphere $\left(KE\right)=576\text{J}$
Moment of inertia of hollow spherical ball about axis passing through its COM $I=\frac{2}{3}m{r}^2$
$=\frac{2}{3}\times 3\times (2{)}^2$
$=8{\text{kg m}}^2$
Kinetic energy, $KE=\frac{1}{2}I{\omega }^2$
$\Rightarrow \omega =\sqrt{\frac{2KE}{I}}=\sqrt{\frac{2\times 576}{8}}=12\text{rad/s}$