Question

Two bodies with moment of inertia $I_1$ and $I_2$ ($I_1>I_2$) have equal angular momentum. If their respective $KE$ of rotation are $E_1$ and $E_2$ then

• A. $E_1>E_2$
• B. $E_1<E_2$
• C. $E_1=E_2$
• D. $E_1=2E_2$

Answer 1

Answer: (B)

$E_1<E_2$

$I_1>I_2$
Let ${\omega }_1$ and ${\omega }_2$ be angular speed.
$I_1{\omega }_1=I_2{\omega }_2.$
$\therefore {\omega }_2>{\omega }_1$
$\therefore KE{)}_{Rotational}=\frac{1}{2}I{\omega }^2.$
$E_1=\frac{1}{2}{I}_1{{\omega }_1}^2,E_2=\frac{E_2}{2}{{\omega }_2}^2.$
$=\left(\frac{I_1{\omega }_1}{2}\right){\omega }_1,E_2=\left(\frac{I_2{\omega }_2}{2}\right){\omega }_2$
$\therefore {\omega }_2>{\omega }_1$
$\therefore E_2>E_1$