A cylinder having radius 0.4 m initially rotating (at `r=0`) with `omega_(0)=54rad//s` is placed on a rough inclined plane with `theta=37^(@)` having friction coefficient `mu=0.5` the time taken by the cylinder to start pure rolling is `(g=10m//s^(2))`

Options

A. 5.4 s
B. 2.4 s
C. 1.4 s
D. none of these

Answer

D

Explanation

`a=(mucostheta)+(gsintheta)`
`=0.5xx10xx0.8+10xx0.6=10m//s^(2)`
`alpha=(mumgcostheta)R)/((1)/(2)mR^(2))=(2mugcostheta)/(R)`
`=(2xx0.5xx10xx0.8)/(0.4)=20rad//s^(2)`
Pure rolling will start when
`v=Romega` or at `=R(omega_(0)-alphat)`
`therefore10t=0.4(54-20t)`
Solving this equation we get
`t=1.2s`