Prove that the fractional loss in kinetic energy for the ball-pendulum system is given by equation 1-m/m+M?

You need to include the introductory sentences of this problem,

the final question is meaningless without them.

that is a flow of momentum via deflection, yet purely the cue-stick can manage what the cue-ball will do after collision. In different words, if the cue-ball is rolling forward(precise spin) that is going to proceed to attain this for a quick era, after collision with the 5-ball. The collision has decreased the cue-balls momentum. If the cue-ball isn't rolling, yet sliding forward(contacted slightly below midsection via the cue-stick), that is going to offer up on the factor of collision with the 5-ball. If opposite spin(backside english) is utilized to the cue-ball, however the momentum remains propelling it forward, that is going to collide with the 5-ball and roll backward.

it fairly is a circulate of momentum by deflection, yet purely the cue-stick can control what the cue-ball will do after collision. In different words, if the cue-ball is rolling forward(ideal spin) it is going to proceed to take action for a short era, after collision with the 5-ball. The collision has decreased the cue-balls momentum. If the cue-ball isn't rolling, yet sliding forward(contacted merely decrease than middle by the cue-stick), it is going to provide up on the factor of collision with the 5-ball. If opposite spin(backside english) is utilized to the cue-ball, however the momentum continues to be propelling it forward, it is going to collide with the 5-ball and roll backward.