You attach a \(0.50-\mathrm{m}\) length of string to a \(50 \mathrm{~g}\) puck and pass the other end of the string through a hole in the center of a table. Grasping the string under the table, you pull just enough string through the hole so that, when your friend gives the puck a sideways push, it moves in a circle of radius \(r_{\mathrm{i}}=0.45 \mathrm{~m}\) at \(1.5 \mathrm{~m} / \mathrm{s}\). You then slowly pull on the string, decreasing the circle's radius to \(0.20 \mathrm{~m}\).

(a) What is the puck's speed when \(r=0.20 \mathrm{~m}\) ? \((b)\) What is the tension in the string as a function of \(r\) ? What is its value when \(r=0.20 \mathrm{~m}\) ?

(c) How much work is done in moving the puck from the \(0.45-\mathrm{m}\) circle to the \(0.20-\mathrm{m}\) circle?