Question

Two bodies with moment of inertia $I_1$ and $I_2$$(I_1>I_2)$ have equal angular momentum. If the KE of rotation is $E_1$ and $E_2$ , then :

• A. $E_1>E_2$
• B. $E_1<E_2$
• C. $E_1=E_2$
• D. none of these

Answer 1

The correct option is B $E_1<E_2$

$I_1>I_2$

$L_1=L_2$

$I_1{\omega }_1=I_2{\omega }_2$ ----(3)

$E_1=\frac{1}{2}{I}_1{{\omega }_1}^2$ ----(1)

$E_2=\frac{1}{2}{I}_2{{\omega }_2}^2$

$E_2=\frac{1}{2}{I}_1{\omega }_1{\omega }_2$ ---(2)

$\frac{E_1}{E_2}=\frac{{\omega }_1}{{\omega }_2}$

$\frac{I_1}{I_2}=\frac{{\omega }_2}{{\omega }_1}>1$

$\therefore \frac{{\omega }_2}{{\omega }_1}>1$

$\therefore \frac{E_1}{E_2}<1$

$\therefore E_1<E_2$