Two bodies A and B have their moments of inertia I 1 and I 2 respectively about their axis of rotation. If their kinetic energies of rotation are equal and their angular momenta L 1 and L 2 re

Question

Two bodies A and B have their moments of inertia I 1 ​ and I 2 ​ respectively about their axis of rotation. If their kinetic energies of rotation are equal and their angular momenta L 1 ​ and L 2 ​ respectively are in the ratio 1 : 3 ​ , then I 2 ​ will be

TestHub · Accepted Answer

The rotational kinetic energy is given by $K = \frac{L ^{2}}{2 I}$ .

Given that the kinetic energies of rotation are equal, $K_{1} = K_{2}$ .

$\frac{L _{1}^{2}}{2 I _{1}} = \frac{L _{2}^{2}}{2 I _{2}}$

Rearranging the terms, we get:

$\frac{I _{2}}{I _{1}} = (\frac{L _{2}}{L _{1}})^{2}$

Given the ratio of angular momenta $\frac{L _{1}}{L _{2}} = \frac{1}{3}$ , substituting this value:

$\frac{I _{2}}{I _{1}} = (3)^{2} = 3$

$I_{2} = 3 I_{1}$

Answer: $3 I_{1}$

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