Question

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

Hint:

Always convert RPM to rad/s by multiplying by $\frac{2\pi}{60}$ before calculating energy.

Answer 1

The Correct Option is A

Step 1: Concept
Kinetic energy in rotational/circular motion can be expressed as $K.E. = \frac{1}{2}mv^{2}$, where $v = r\omega$.

Step 2: Unit Conversion
Angular speed $\omega = 300~RPM$.
$\omega = 300 \times \frac{2\pi}{60} = 10\pi~rad/s$.

Step 3: Calculation
Linear velocity $v = r\omega = 1 \times 10\pi = 10\pi~m/s$.
$K.E. = \frac{1}{2}(5)(10\pi)^{2} = \frac{1}{2}(5)(100\pi^{2}) = 250\pi^{2}~J$.

Step 4: Conclusion
The kinetic energy is $250\pi^{2}$. Final Answer: (A)