First slide

General Planar motion

Question

Two rigid bodies A and B rotate with angular momenta L_A and L_B, respectively. The moments of inertia of A and B about the axes of rotation are I_A and I_B respectively. If $I_{A} = I_{B} / 4 and L_{A} = 5 L_{B}$ ,then the ratio of rotational kinetic energy K_A of A to the rotational kinetic energy K_B of B is given by

Easy

A

$\frac{K_{A}}{K_{B}} = \frac{25}{4}$
B

$\frac{K_{A}}{K_{B}} = \frac{5}{4}$
C

$\frac{K_{A}}{K_{B}} = \frac{1}{4}$
D

$\frac{K_{A}}{K_{B}} = 100$

Solution

$\begin{array}{l} K_{A} = \frac{L_{A}^{2}}{2 l_{A}} = \frac{25 L_{B}^{2}}{2 (\frac{l_{B}}{4})} \\ K_{B} = \frac{L_{B}^{2}}{2 l_{B}} \\ Now, \frac{K_{A}}{K_{B}} = 25 \times 4 = 100 \end{array}$

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