A disc of circumference `s` is at rest at a point `A` on a horizontal surface when a constant horizontal force begins to act on its centre. Between `A` and `B` there is sufficient friction toprevent slipping, and the surface is smooth to the right of `B.AB = s`. The disc moves from `A` to `B` in time `T`. To the right of `B`,
.

Options

A. the angular acceleration of the disc will disappear linear acceleration will remain unchanged
B. . linear acceleration of the disc will increase
C. the disc will make one rotation in time `T//2`
D. the disc will cover a distance greater than s in further time `T`

Answer

B, C, D

Explanation

Let `P=`external force `F=` force of friction between `A` and `B` `a_(1)=` acceleration between `A` and `B a_(2) =` acceleration beyond `B`
`P-F=ma_(1)`
`P=ma_(2`
`a_(2)gta_(1)`
Let `alpha=`angualar acceleration between `A` and `B`
For one rotation `theta=2pi=1/2alphaT^(2)`
`T=sqrt((4pi)/alpha)= ` time of travel from `A` to `B`
angular velocity at `B=omega_(0)=alphaT`
For one rotation to the right of `B`
`theta=2pi=omega_(B)t`
`t=(2pi)/(aT)=(1/2alphaT^(2))/(alphaT)=T/2`