Problem $2[17$ points$]$

Consider a solid ball of mass $M$ and radius $R$ released from rest at a height $H.$ The ball rolls without slipping down the slope, as shown in the figure. At the bottom of the ramp, the coefficient of friction abruptly changes from $$ on the left to a very small value on the right, making the right side of the ramp effectively frictionless.

$($a$)$ Determine the speed of the ball at it lowest height.

$($b$)$ Determine the height, $h_R,$ that the ball reaches on the right side of the ramp.

$($c$)$ Qualitatively describe what would happen in the ball was released from the right side of the ramp at height $h_R,$ as calculated in $($b$).$ Include a description of what happens at the bottom amd comment on the height reached on the left side of the ramp. There is no need for a calculation; simply present your response by referring to any relevant physical principles.