Question

The rotational kinetic energy of a body is $ {{K}_{rot}} $ and its moment of inertia is $ I $ . The angular momentum of body is:

• A. $ I{{K}_{rot}} $
• B. $ 2\sqrt{I{{K}_{rot}}} $
• C. $ \sqrt{2I{{K}_{rot}}} $
• D. $ 2I{{K}_{rot}} $

Answer 1

Answer: (C)

The rotational kinetic energy of a body is given by
$ K_{\text {rot }}=\frac{1}{2} I \omega^{2} $
$\Rightarrow I \omega^{2}=2 K_{\text {rot }} $
$\Rightarrow \omega=\sqrt{\frac{2 K_{\text {rot }}}{I}}$
Angular momentum of body is given by
$J =I \omega \equiv I \times \sqrt{\frac{2 K_{ rot }}{I}} $
$=\sqrt{2 K_{\text {rot }} I}$