Two bodies A and B have moment of inertia I A and I B , and angular momenta L A and L B respectively. Both of them have same kinetic energy of rotation. So the ratio L A to L B is

Question

Two bodies A and B have moment of inertia I A ​ and I B ​ , and angular momenta L A ​ and L B ​ respectively. Both of them have same kinetic energy of rotation. So the ratio L A ​ to L B ​ is

TestHub · Accepted Answer

The rotational kinetic energy of a body is given by $K = \frac{L ^{2}}{2 I}$ , where $L$ is the angular momentum and $I$ is the moment of inertia.

Given that both bodies have the same rotational kinetic energy, $K_{A} = K_{B}$ .

$\frac{L _{A}^{2}}{2 I _{A}} = \frac{L _{B}^{2}}{2 I _{B}}$

$\frac{L _{A}^{2}}{L _{B}^{2}} = \frac{I _{A}}{I _{B}}$

Taking the square root on both sides, we get:

$\frac{L _{A}}{L _{B}} = \frac{I _{A}}{I _{B}}$

Answer: $\frac{I _{A}}{I _{B}}$

Physics - Rotation Question with Solution | TestHub

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