### Problem 4: Rolling Cylinder on a TrackA cylinder \((I_{\text{cm}} = MR^2/2)\) starts from rest at height \(H\) at the upper end of the track shown in the diagram. It rolls without slipping until it leaves the horizontal portion of the track at height \(h\) as depicted.#### Diagram Explanation:- The diagram is a simple track illustration. It shows a vertical drop from height \(H\) leading into a curved section, finally transitioning into a straight horizontal segment ending at height \(h\). At the top, a cylinder is positioned to roll down.#### Questions:(a) What is the cylinder's linear speed as it leaves the track?(b) How does its kinetic energy, associated with this speed, compare to its change in gravitational potential energy from \(H\) to \(h\)?(c) How far to the right does the cylinder land from the end of the track?

Answered: Image /qna-images/answer/c988edeb-bbe5-4f8d-8fa9-0fc798840c81.jpg

A cylinder [Im = MR/2] starts from rest at height H at the upper end of the track shown, and rolls without slipping until H leaving the horizontal portion of track at height h as shown. (a) What is the cylinder's linear speed as it leaves the track? (b) How does its kinetic energy associated with this speed compare to its change in gravitational potential energy from H to h? (c) How far to the right does the cylinder land from the end of the track?

A cylinder [Im = MR/2] starts from rest at height H at the upper end of the track shown, and rolls without slipping until H leaving the horizontal portion of track at height h as shown. (a) What is the cylinder's linear speed as it leaves the track? (b) How does its kinetic energy associated with this speed compare to its change in gravitational potential energy from H to h? (c) How far to the right does the cylinder land from the end of the track?