A 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?

Options

A. 28.16 rad/sec
B. 19.28 rad/sec
C. 8.12 rad/sec
D. 35.26 rad/sec

Answer

A

Explanation

Mass (m) = 2 kg ,
initial radius of the path `(r_(1)) = 0.8` m , initial angular velocity (`omega_(1))` = 44 rad/sec and final radius of the path `(r_(2)) = 1` m
Initial moment of inertia , `I_(1) = m r_(1)^(2) = 2 xx (0.8)^(2) = 1.28 kg m^(2)`
and final moment of inertia , `I_(2) = mr_(2)^(2) = 2 xx (1)^(2) = 2 kg m^(2)`
From the law of conservation of angular momentum
`I_(1) omega_(1) = I_(2) omega_(2) or omega_(2) = (I_(1) omega_(1))/(I_(2)) = (1.28 xx 44)/(2) = 28.16` rad/sec