A whel of mass 2kg an radius 10 cm is rotating about its axis at an angular velocity of `2pirad//s` the force that must be applied tangentially to the wheel to stop it in 5 revolutions is

Options

A. `3pixx10^(-2)kg-m^(2)//s`
B. `4pixx10^(-2)kg-m^(2)//s`
C. `pixx10^(-2)kg-m^(2)//s`
D. `2pixx10^(-2)kg-m^(2)//s`

Answer

D

Explanation

Moment of inertial of wheel about its axis
`l=(mR^(2))/(2)=(2xx(0.1)^(2))/(2)=0.01kg-m^(2)`
Now angular displacement `Deltatheta=2pin=2pixx5=10pirad`
`therefore` angular retardation required `alpha=(omega^(2))/(2Deltatheta)=((2pi)^(2))/(2xx10^(pi))=pi//5rad//s^(2)`
`therefore` Torque required `tau=lalphaimpliesFR=lalpha`
`thereforeF=(lalpha)/(R)=(0.01)/(0.10)xx(pi)/(5)=2pixx10^(-2)N`