Question

A sphere rotating about it diameter has rotational K.E of 360J its angular speed is 30 radls its M.I is

Answer 1

➡️➡️Since it is rotating then only take rotational kinetic energy.

Rotational K.E.
$kinetic \: energy = \frac{1}{2} i \: {w}^{2} \\ \\ 360 = \frac{1}{2} i {(30)}^{2} \\ i = \frac{720}{900}$
Hope it will help you‼️

Answer 2

Given :

Kinetic energy of sphere about diameter , K.E = 360 J .

Angular speed of sphere , $\omega=30\ rad/s$ .

To Find :

The moment of inertia of sphere .

Solution :

We know , rotational kinetic energy is given by :

$K.E=\dfrac{I\omega^2}{2}\\\\360=\dfrac{I\times 30^2}{2}\\\\I=\dfrac{360\times 2}{30^2}\\\\I=0.8\ kg\ m^2$

Hence , this is the required solution .

Learn More :

Moment of inertia

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