A pendulum of mass m is held horizontally as shown in the figure. The massless string of length L= d+r is held taut, and the pendulum is released. At the bottom of the path of the pendulum, the string comes into contact with a peg positioned a vertical distance d from the point of suspension of the pendulum. (a) Just before the string comes into contact with the peg, derive an expression for the speed of the pendulum bob. Your expression may contain some or all of the following quantities: m, g, L, d, r. (b) Derive an expression for the tension in the string just before the string comes into contact with the peg. Your expression may contain some or all of the following quantities: m, g, L, d, r. (c) What is the speed of the pendulum just after the string hits the peg? (d) What is the tension of the string just after the string hits the peg. (e) After the string hits the peg, what is the maximum height that is acheived by the pen- dulum bob. What speed does it have at this point? (f) The string will break if the tension in the string exceeds 9mg. What is the largest value of r that will result in the string breaking. Your expression for r should be expressed as a fraction of the string length L. m L d peg