Question

The moments of inertia of two rotating bodies $A$ and $B$ are $I_A$ and $I_B(I_A>I_B)$. If their angular momenta are equal, then

• A. Kinetic energy of $A=$ Kinetic energy of $B$
• B. Kinetic energy of $A>$ Kinetic energy of $B$
• C. Kinetic energy of $A<$ Kinetic energy of $B$
• D. Kinetic energy of the two bodies cannot be compared with the given data

Answer 1

Answer: (C)

$I_A{\omega }_A=I_B{\omega }_B$ (Given)
$\therefore \frac{{\omega }_A}{{\omega }_B}=\frac{I_B}{I_A}...\left(i\right)$
Kinetic energy $=\frac{1}{2}I{\omega }^2$
$\therefore \frac{{\left(K.E\right)}_A}{{\left(K.E\right)}_B}=\frac{\frac{1}{2}{I}_A{\omega }_A^2}{\frac{1}{2}{I}_B{\omega }_B^2}$ (Using $(i)$)
$=\frac{I_A}{I_B}\times {\left(\frac{I_B}{I_A}\right)}^2$
$=\frac{I_B}{I_A}$
As $I_A>I_B$ (Given)
$\therefore {\left(K.E\right)}_A<{\left(K.E\right)}_B$