Question

Two rotating bodies $A$ and $B$ of masses m and 2m with moments of inertia $I_A$ and $I_B$ $(I_B>I_A)$ have equal kinetic energy of rotation. If $L_A$ and $L_B$ be their angular moment a respectively, then:

• A. $L_A=\frac{L_B}{2}$
• B. $L_A=2L_B$
• C. $L_B>L_A$
• D. $L_A>L_B$

Answer 1

The correct option is C $L_B>L_A$

$m_A=m$, $m_B=2m$

A, B have equal kinetic energy of rotation|

$k_A=k_B$

$\Rightarrow \frac{1}{2}{I}_A{w}_{A^2}=\frac{1}{2}{I}_B{w}_{B^2}$

$\frac{w_{A^2}}{w_{B^2}}=\frac{I_B}{I_A}$ ......$\left(1\right)$

Ratio of angular momenta,

$\frac{L_A}{L_B}=\frac{I_A{w}_A}{I_B{w}_B}=\frac{I_A}{I_B}\times \sqrt{\frac{I_B}{I_A}}=\sqrt{\frac{I_A}{I_B}}<1$

$(I_B>I_A)$

$L_B>L_A$.