Question

26. If the angular velocity of a body increases by 20%,
then its kinetic energy of rotation will increase by
(a) 20%
(b) 30%
(c) 44%
(d) 66%​

Answer 1

Explanation:

EK=1/2MV²

EK=26/20*100

=44%

Answer 2

Answer:

The correct answer is Option C: $44$%

Explanation:

It is given that the angular velocity increases by $20\%$.

The kinetic energy can be expressed as:

$KE=\frac{1}{2}I\omega^2$

The initial conditions can be expressed as:

$\omega=\omega_1\\\\K=K_1$

The final conditions can be expressed as:

$\omega=\omega_2\\\\K=K_2$

$\omega$ increases by $20\%$

$\omega_2=\omega_1+0.2\omega_1\\\omega_2=1.2 \omega_1$

Kinetic energy in initial and final conditions:

$K_1=\frac{1}{2} I\omega_1^2\\\\K_2=\frac{1}{2} I(1.2\omega_1)^2$

$K_2=1.44 * \frac{1}{2} I\omega_1^2$

We can substitute $K_1$ in the above equation.

$K_2=1.44K_1$

Now, to find the percentage :

$\frac{K_2-K_1}{K_1} *100\\\\=\frac{1.44K_1-K_1}{K_1} *100\\\\=44\%$

Hence, the kinetic energy increases by $44\%$.

Angular velocity:

In physics, the rotational velocity or angular velocity, also referred to as the angular frequency vector, is a pseudovector that illustrates how quickly an object's angular location or orientation varies over time.

Kinetic energy:

An object's rotation generates kinetic energy, also known as angular kinetic energy, which is a component of the object's overall kinetic energy.