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Rotational Motion question

2016 · Q147
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Rotational Motion question

2016 · Q147

NEETPhysicsRotational MotionMCQ+4 / −1
Two rotating bodies A and B of masses m and 2m with moments of inertia IA{I_A}IA​ and IB{I_B}IB​ (IB{I_B}IB​ > IA{I_A}IA​) have equal kinetic energy of rotation. If LA and LB be their angular momenta respectively, then
  1. A
    LA=LB2{L_A} = {{{L_B}} \over 2}LA​=2LB​​
  2. B
    LA=2LB{L_A} = 2{L_B}LA​=2LB​
  3. C
    LB>LA{L_B} \gt {L_A}LB​>LA​
  4. D
    LA>LB{L_A} \gt {L_B}LA​>LB​
View written solutionFree

Correct answer: C

It is known that rotational kinetic energy is given as :

E=Iω22E = {{I{\omega ^2}} \over 2}E=2Iω2​ = L22I{{{L^2}} \over {2I}}2IL2​

Hence, L2 ∝\propto∝ I

Further, EA = EB

Also, LA22IA=LB22IB{{{L_A}^2} \over {2{I_A}}} = {{{L_B}^2} \over {2{I_B}}}2IA​LA​2​=2IB​LB​2​

IB>IA{I_B} \gt {I_A}IB​>IA​

LB>LA{L_B} \gt {L_A}LB​>LA​

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