Question

Two identical masses each of mass m = 2 kg are connected to a light rod, of length 2 m and rotated with angular velocity = √10 rad/s about vertical axis as shown in figure. The kinetic energy of the system is (g = 10 m/s²)​

Answer 1

Given:

Two identical masses each of mass m = 2 kg are connected to a light rod, of length 2 m and rotated with angular velocity = √10 rad/s about vertical axis.

To find:

Net kinetic energy of the system?

Calculation:

So, the kinetic energy will be rotational KE.

$\rm KE = \dfrac{1}{2} \times I_{total} \times { \omega}^{2}$

$\rm \implies KE = \dfrac{1}{2} \times (m {r}^{2} + m {r}^{2} ) \times { \omega}^{2}$

• 'r' is distance of mass from axis.

$\rm \implies KE = \dfrac{1}{2} \times (2m {r}^{2}) \times { \omega}^{2}$

$\rm \implies KE = m {r}^{2} \times { \omega}^{2}$

$\rm \implies KE = 2 \times {(1)}^{2} \times {( \sqrt{10}) }^{2}$

$\rm \implies KE = 20 \: joule$

So, net KE is 20 Joules.