A $2\mathrm{.}00$ Kg uniform solid sphere is rolling without slipping along a horizontal surface with a speed of $5\mathrm{.}00$ m$/$s when it starts up a ramp that makes an angle of $30\mathrm{.}0$ with the horizontal. The sphere has a radius of $0\mathrm{.}50$ m$.$ Moment of inertia of the solid sphere is I$=25$mr$2.$

a$)$ What is the total kinetic energy of the sphere when it starts up a ramp?

b$)$ What is the maximum altitude reaching by the sphere? $($Tip: using the law of conservation of energy$)$

c$)$ How many meters the sphere rolled along the surface of the ramp when the sphere reach the maximum altitude?

d$)$ Home many revolutions complete the sphere in its rolling motion up$?$