Question

If 2 kg mass is rotating on a circular path of radius 0.8 m with angular velocity of 44 rad/sec. If radius of the path becomes 1 m, then what will be the value of angular velocity?

(a) 28.16 rad/sec 

(b) 19.28 rad/sec

(c) 8.12 rad/sec 

(d) 35.26 rad/sec

Answer 1

Correct option (a) 28.16 rad/sec 

Explanation :

Mass (m) = 2 kg; initial radius of the path

(r₁) = 0.8 m; initial angular velocity

(ω₁) = 44 rad/sec and final radius of the path

(r₂) = 1 m,

Moment of inertia, I₁ =  mr₁² = 2 x (0.8)²

= 1.28 kg m² and I₂ = mr₂² = 2 x (1)² = 2kg m² 

Therefore from the law of conservation of angular momentum,