In figure wheel `A` of radius `r_A = 10 cm` is coupled by belt `B` to wheel `C` of radius `r_C = 25 cm`. The angular speed of wheel `A` is increased from rest at a constant rate of `1.6 rad//s^2`. Find the time needed for wheel `C` to reach an angular speed of `12.8 rad//s`, assuming the belt does not slip.
.

Options

A. `20 sec`
B. `10 sec`
C. `1.5 sec`
D. `15 sec`

Answer

A

Explanation

At any instant linear acceleration of all points of coupled belt is same. `a=r alpha`
`r_(1)alpha_(1)=r_(2)alpha_(2),` find `alpha_(2), omega_(2)=omega_(1)+alpha_(2)t`
`t=(omega_(2))/(alpha_(2)) :' omega_(1)=0`