InterviewSolution
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InterviewSolution
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Two bodies with moments of inertia I1 and I2 (I1 > I2) rotate with the same angular momentum. If E1 and E2 are their rotational kinetic energies, then(A) E2 > E1 (B) E2 = E1(C) E2 < E1(D) E2 ≤ E1 |
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Answer» Correct option is (A) \(E_2 > E_1\) Angular Momentum \(L = I \omega\) Given, \(I_1 = I_2\) \(I_1 \omega_1 = I_2 \omega_2\) \(\frac{\omega_1}{\omega_2} = \frac{I_2}{I_1}\) Kinetic Energy K.E = \(\frac{1}{2} I\omega^2\) \(\frac{E_1}{E_2} = \frac{I_1}{I_2} (\frac{\omega_1}{\omega_2})^2\) \(\frac{E_1}{E_2} = (\frac{I_1}{I_2}) (\frac{\omega_1}{\omega_2})^2\) \(\frac{E_1}{E_2} = \frac{I_1}{I_2} \times \frac{I_2{^2}}{I_1{}^2}\) \(\frac{E_1}{E_2} = \frac{I_2}{I_1}\) Given, \(I_1 > I_2\) then, \(E_2 > E_1\) Correct option is (A) E2 > E1 |
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