Question

Two bodies, $A$ and $B$ with moment of inertia $I_A$ and $I_B(I_B>I_A)$ have equal rotational kinetic energy are rotating about the same axis. If $L_A$ and $L_B$ be their angular momentum 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 $L_B>L_A$

We know that the relation between rotational kinetic energy and angular momentum is given by:
$E=\frac{L^2}{2I}$, where,
$E\to$ rotational kinetic energy
$L\to$ angular momentum
​​​​​​​$I\to$ moment of inertia
Given, rotational kinetic energies of the two bodies are equal.
So, $\frac{L_A^2}{2I_A}=\frac{L_B^2}{2I_B}$
$\Rightarrow \frac{I_B}{I_A}=\frac{L_B^2}{L_A^2}$
$\Rightarrow L_B>L_A$ $[\because I_B>I_A]$