Question $4(20$ marks$)$

The disk in Figure Q$4$ has a mass of $10-$kg and a radius of gyration of k$\_($G$)=\backslash$sqrt$(0\mathrm{.}02)$m

about its center of mass G$.$ The disk is at rest before the horizontal force P$=60$N is

applied to its mass center G$.$ The coefficients of static and kinetic friction for the surfaces

in contact are $\backslash$mu $\_($s$)=0\mathrm{.}2$ and $\backslash$mu $\_($k$)=0\mathrm{.}15,$ respectively.

$($i$)$ Which two possible motions of the disk are possible?

$($ii$)$ Calculate the maximum possible static friction force.

$($iii$)$ Calculate the actual static friction force assuming that the disk rolls without

slipping after the $60-$ N force is applied. Comment on your answer.

$($iv$)$ Hence or otherwise, determine the angular acceleration of the disk and the

acceleration of G$.$

$[2+3+8+7$ marks $]$