Question

A mass of $5\text{kg}$ is moving along a circular path of radius 1 m. If the mass moves with 300 revolutions per minute, its kinetic energy would be

• A. $250{\pi }^{2}J$
• B. $100{\pi }^{2}J$
• C. $5{\pi }^{2}J$
• D. 0

Answer 1

The correct option is A $250{\pi }^{2}J$

According to the problem, Radius = 1 m, Mass (m)
$m=5\text{kg}$, Frequency of revolution, f = 300 rev/min
$f=\frac{300}{60}$
Angular velocity will be
$=2\pi f=(300\times 2\pi )\text{rad/min}$
$=(300\times 2\times 3.14)\text{rad}/60s$
$=\frac{300\times 2\times 3.14}{60}\text{rad/s}=10\pi \text{rad/s}$
And relation between linear velocity and angular velocity is, $v=\omega R$
$=10\pi \left(1m\right)$
$=10\pi \text{m/s}$
And kinetic energy $=\frac{1}{2}m{v}^2$
$=250{\pi }^{2}J$
Hence, the correct answer is option (a).