A pulley os radius 2m is rotated about its axis by a force `F= (20 t- 5t^2)` newton (where t is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation is `10kg m^2` the number of rotaitons made by the pulley before its direction of motion is reversed, is:

Options

A. Less than 3
B. More than 3 but less than 6
C. More than 6 but less than 9
D. More than 9

Answer

B

Explanation

`F=(20t-5t^(2))N`, `I=10kg-m^(2)`, `r=2m`
`tau=Fr=2(20t-5t^(2))`
`tau=I alphaimpliesalpha=(20t-5t^(2))/(10)`
`implies(d omega)/(dt)=4t-t^(2)`
`impliesint d omega=int(2t-t^(2))dtimpliesomega=2t^(2)-(t^(3))/(3)`
`omega=0impliest=6sec`
`theta=intomega dt=int_(0)^(6)(2t^(2)-(t^(3))/(3))dt=36rad`
No. of revolution `=(36)/(2pi) lt 6`.