Question

 If the angular velocity of a body rotating about a given axis is doubled , then its rotational K.E *

1 point

a) is doubled

b) is halved

c) becomes four times

d)becomes one - fourthin​

Answer 1

Rotational Kinetic energy of a particle is defined as:-

$\large \red{\underline{ \frac{1}{2} \Iota {\omega}^{2} }}$

Here:-

$I = \blue{moment \: of \: inertia}$

$\omega= \blue{angular \: velocity}$

Now according to question

→ Angular speed is doubled.

The new Rotational KE becomes

$\large \green{\underline{ \frac{1}{2} \Iota {(2\omega})^{2} }}$

→

$\large \green{4 \times { \frac{1}{2} \Iota {\omega}^{2} }}$

Hence Rotational KE becomes 4 times.

C option is correct

Answer 2

Given : Angular velocity of a body rotating about a given axis is doubled.

To Find : Rotational K.E.

Explanation:

Rotational kinetic energy

$\[K.E= \frac{1}{2}I{W^2}\]$

W =angular velocity

 I = Moment of inertia

Thus,

$\[K.{E_2} = \frac{1}{2}I \times {W_1}^2\]$

As when anglular velocity is doubled

Then , $\[{W_2} = 2{W_1}\]$

Thus putting it when angular velecity is doubled.

$\[K.{E_2} = \frac{1}{2}I \times {(2{W_1})^2}\]$                        (As  $\[{W_2} = 2{W_1}\]$)

$\[K.{E_2} = 4K.E{._1}\]$

Hence,  Rotational Kinetic energy c) becomes four times.