A fly wheel having a moment of inertia of `10^(7) g cm^(2)` and revolving at the rate of 120 rpm is stopped by a brake in course of 5 seconds. Find the controlling torque.

Options

A. `2.51 xx 10^(7)` dyne-cm
B. `5.21 xx 10^(7)` dyne-cm
C. `1.25 xx 10^(7)` dyne-cm
D. `2.15 xx 10^(5)` dyne-cm

Answer

A

Explanation

Obviously, the controlling torque will produce a retardation of the fly wheel. Let a. be the angular retardation produced by the application of the torque.
Initial angular speed of the fly wheel,
`omega_(1)=(2pir)/60=(2pixx120)/60=4pi"rad"//"sec"`
Final angular speed = `omega_(2) = 0`, time= t = 5 sec.
Now, applying the formula `omega_(2) = omega_(1) - alphat`, we get
`0=4pi-alphaxx5` or `alpha=(4pi)/5` rad/se`c^(2)`
We know, torque = moment of Inertia (I) `xx alpha`
`therefore` Torque, `tau=10^(7)xx(4pi)/5=2.51xx10^(7)` dyne cm