SATHEE: Rotational Motion Question 59

Rotational Motion Question 59

Question: Two bodies have their moments of inertia $l$ and $2 l$ respectively about their axis of rotation. If their kinetic energies of rotation are equal, their angular momenta will be in the ratio:

[AIPMT (S) 2005]

Options:

A) 1 : 2

B) $\sqrt{2} : 1$

C) 2 : 1

D) $1 : \sqrt{2}$

Show Answer

Answer:

Correct Answer: D

Solution:

As said, ${(K E)}_{r o t}$ remains same. i.e., $\frac{1}{2} I_{1} ω_{1}^{2} = \frac{1}{2} I_{2} ω_{2}^{2}$

$\Rightarrow$ $\frac{1}{2 I_{1}} {(I_{1} ω_{1})}^{2} = \frac{1}{2 I_{2}} {(I_{2} ω_{2})}^{2}$

$\Rightarrow$ $\frac{L_{1}^{2}}{I_{1}} = \frac{L_{2}^{2}}{I_{2}}$

$\Rightarrow$ $\frac{L_{1}}{L_{2}} = \sqrt{\frac{I_{1}}{I_{2}}}$ but $I_{1} = I, I_{2} = 2 I$

$∴$ $\frac{L_{1}}{L_{2}} = \sqrt{\frac{I}{2 I}} = \frac{1}{\sqrt{2}}$ or $L_{1} : L_{2} = 1 : \sqrt{2}$

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Rotational Motion Question 59

Question: Two bodies have their moments of inertia l and 2l respectively about their axis of rotation. If their kinetic energies of rotation are equal, their angular momenta will be in the ratio:

Options:

Answer:

Solution:

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Question: Two bodies have their moments of inertia $l$ and $2 l$ respectively about their axis of rotation. If their kinetic energies of rotation are equal, their angular momenta will be in the ratio: