A mass of \(5~\text {kg}\) is moving along a circular path of radius \(1~\text {m}\). If the mas moves with \(300~\text {rev/min}\), its kinetic energy would be
1. \(250 \pi^2~\text{J}\)
2. \(100 \pi^2~\text{J}\)
3. \(5 \pi^2~\text{J}\)
4. \(0\)

(a) Hint: Using angular velocity, we can find the linear speed.

Step 1: Find the angular speed of the mass.

 Given,mass=m=5kg
Radius=1m=R
Revolutionpermin.ω=300rev/min
=(300×2π)rad/min
=(300×2×3.14)rad/60s
=300×2×3.1460rad/s=10πrad/s

Step 2: Find the kinetic energy of the mass.

⇒    linear speed =v=ωR=(300×2π60)(1)=10πm/sKE=12mv2=12×5×(10π)2=100π2×5×12=250π2J