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Rotational Motion question

2005 · Q163
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Rotational Motion question

2005 · Q163

NEETPhysicsRotational MotionMCQ+4 / −1
Two bodies have their moments of inertia I and 2I respectively about their axis of rotation. If their kinetic energies of rotation are equal, their angular velocity will be in the ratio
  1. A
    2 : 1
  2. B
    1 : 2
  3. C
    2:1\sqrt 2 :12​:1
  4. D
    1:21:\sqrt 21:2​
View written solutionFree

Correct answer: C

K.E.=12Iω2K.E. = {1 \over 2}I{\omega ^2}K.E.=21​Iω2

∴12I1ω12=12.2I1ω22 \therefore {1 \over 2}{I_1}\omega _1^2 = {1 \over 2}.2{I_1}\omega _2^2∴21​I1​ω12​=21​.2I1​ω22​

ω12ω22=21⇒ω1ω2=21{{\omega _1^2} \over {\omega _2^2}} = {2 \over 1} \Rightarrow {{{\omega _1}} \over {{\omega _2}}} = {{\sqrt 2 } \over 1}ω22​ω12​​=12​⇒ω2​ω1​​=12​​

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