$4.$ A $\backslash (15-\backslash$mathrm$\{$kg$\}\backslash )$ roll of wrapping paper in the form of a solid cylinder with a diameter of $300$ mm is resting on a horizontal surface. If a force of $40$ N is applied to the paper at the angle $\backslash (\backslash$boldsymbol$\{\backslash$theta$\}=30^\{\backslash$circ$\}\backslash ),$ determine the initial acceleration $\backslash ($ a $\backslash )$ of the centre of the roll and the corresponding angular acceleration $\backslash (\backslash$boldsymbol$\{\backslash$alpha$\}\backslash ).$ The coefficient of kinetic friction between the paper and the horizontal surface is $0\mathrm{.}2.$