A constant horizontal force vec$(F{)}_{\text{a}\text{p}\text{p}}$ of magnitude $12\mathrm{.}0$ N is applied to a uniform solid cylinder, which is initially at rest, by a fishing line wrapped around the cylinder. The mass of the cylinder is $10\mathrm{.}0$ kg $,$ its radius is $10\mathrm{.}0$ cm$.$

a$)$ Compute the torque ${}_{\text{a}\text{p}\text{p}}$ on the cylinder from the applied force. $(1$ point$)$

b$)$ Compute the moment of inertia of the cylinder. $(1$ point$)$

c$)$ Compute the angular acceleration of the cylinder. $(1$ point$)$

d$)$ What is the rotational displacement $$ of the cylinder after $t=5\mathrm{.}00s?(1$ point$)$

e$)$ How many meters $x$ of fishing line come off the cylinder in this $t=5\mathrm{.}00s?(1$ point$)$

f$)$ What is the kinetic energy of the cylinder after $t=5\mathrm{.}00s?(1$ point$)$