A wheel whose moment of inertia is 2 kg `m^(2)` has an initial angular velocity of 50 rad/s. A constant torque of 10 Nm acts on the wheel. The time in which the wheel is accelerated to 80 rad's is

Options

A. 12 s
B. 3 s
C. 6 s
D. 9 s

Answer

C

Explanation

Initial angular velocity = 50 rad/s
Final angular velocity = 80 rad/s , Torque = 10 N m
Moment of inertia = 2 kg `m^(2)`
Angular acceleration `alpha` is given by
`alpha = (tau)/(l) = (10)/(2) =5 rad//s^(2) (as rau = I alpha)`
Hence if t is the time ,
`5t = 80 - 50 = 30 or t = 6s`