First slide

Rotational motion

Question

Two bodies with moments of inertia $I_{1} and I_{2} (I_{1} > I_{2})$ have equal angular momenta. If their kinetic energies of rotation are E₁ and E₂, respectively, then

Easy

A

$E_{1} = E_{2}$
B

$E_{1} < E_{2}$
C

$E_{1} > E_{2}$
D

$E_{1} \geq E_{2}$

Solution

$\begin{array}{l} E_{1} = \frac{1}{2} I_{1} ω_{1}^{2} = \frac{1}{2} (I_{1} ω_{1}) ω_{1} = \frac{1}{2} k ω_{1} \\ Now I_{1} ω_{1} = I_{2} ω_{2} = k (say) \\ E_{2} = \frac{1}{2} I_{2} ω_{2}^{2} = \frac{1}{2} (I_{2} ω_{2}) ω_{2} = \frac{1}{2} k ω_{2} \\ I_{1} > I_{2} and ω_{2} > ω_{1} \\ so, E_{2} > E_{1} \end{array}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App