Question

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 momenta will be in the ratio:

पर्याय

• 2 : 1

• 1 : 2

• ${\displaystyle \sqrt{2}:1}$

• ${\displaystyle 1:\sqrt{2}}$

Answer 1

${\displaystyle 1:\sqrt{2}}$

Explanation:

K = ${\displaystyle \frac{{\text{L}}^2}{2\text{I}}}$

⇒ L² = 2KI

⇒ L = ${\displaystyle \sqrt{2\text{KI}}}$

${\displaystyle \frac{{\text{L}}_1}{{\text{L}}_2}=\sqrt{\frac{{\text{K}}_1}{{\text{K}}_2}\cdot \frac{{\text{I}}_1}{{\text{I}}_2}}}$

= ${\displaystyle \sqrt{\frac{\text{K}}{\text{K}}\cdot \frac{\text{I}}{2\text{I}}}}$

= ${\displaystyle \frac{1}{\sqrt{2}}}$

⇒ L₁ : L₂ = ${\displaystyle 1:\sqrt{2}}$