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Two bodies have their moments of inertia `I` and `2 I` respectively about their axis of rotation. If their kinetic energies of rotation are equal, their angular momenta will be in the ratio.A. `1 : 2`B. `sqrt(2) : 1`C. `2 : 1`D. `1 : sqrt(2)` |
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Answer» Correct Answer - D (d) As said, `(KE)_(rot)` remains same. i.e., `(1)/(2) I_1 omega_1^2 = (1)/(2) I_2 omega_2^2` `rArr (1)/(2 I_1)(I_1 omega_1)^2 = (I)/(2 I_2) (I_2 omega_2)^2` `rArr (L_1^2)/(I_1) = (L_2^2)/(I_2)` `rArr (L_1)/(L_2) = sqrt((I_1)/(I_2))` but `I_1 = I, I_2 = 2 I` :. `(L_1)/(L_2) = sqrt((I)/(2 I)) =(1)/(2)` or `L_1 : L_2 = 1 : sqrt(2)`. |
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