Question

Two rigid bodies A and B rotate with rotational kinetic energies $E_A$ and $E_B$ respectively. The moments of inertia of A and B about the axis of rotation are $I_A$ and $I_B$ respectively. If $I_A=I_B/4$ and $E_A/100=E_B$ the ratio of angular momentum $\left(L_A\right)$ of A to the angular momentum $\left(L_B\right)$ of B is

• A. 25
• B. 5/4
• C. 5
• D. 1/4

Answer 1

Answer: (C)

5

$E_{rotational}=\frac{1}{2}I{w}^2=\frac{L^2}{2I}(where,L=Iw)$

Therefore, $L^2=2EI$

Hence,

$\Rightarrow {L_A}^2=2E_A{I}_A$ ........ (1)

$\Rightarrow {L_B}^2=2E_B{I}_B$ ........ (2)

From equation (1) and (2)

$\Rightarrow \frac{L_A}{L_B}=5$