There are two pendulums with bobs having indencital size and mass. The pendulum A is released from rest in the position as shown in the figure. If the maximum angle formed by cord BO' with vertical in the subsequent motion of sphere B is equal to the angle theta_(0) If the coefficient of restitution between sphere A and sphere B is l. find a. the velocities of sphere A and sphere B just after collisions b. the ratio of lengths of pendulums l_B//l_A.

There are two pendulums with bobs having indencital size and mass. The

1.	There are two pendulums with bobs having indencital size and mass. The pendulum A is released from rest in the position as shown in the figure. If the maximum angle formed by cord BO' with vertical in the subsequent motion of sphere B is equal to the angle theta_(0) If the coefficient of restitution between sphere A and sphere B is l. find a. the velocities of sphere A and sphere B just after collisions b. the ratio of lengths of pendulums l_B//l_A.
Answer» Solution :Velocity of `A` just before collision `v_(0)=sqrt(2gl_(A)(1-costheta_(A))`………..i Collision of `A` and `B` Using C.O.L.M. , `m.v_(0)+0=mv_(A)+mv_(B)` `v_(A)+v_(B)=v_(0)`……ii Using NEWTON's restitution law `v_(B)-v_(A)=v_(0)` `v_(B)-v_(A)=ev_(0)`………ii Solving EQN i and ii `v_(A)=(v_(0))/2(1-e)` and `v_(B)=(v_(0))/2(1+e)` As `B` swings angle `thetaB`, hence `v_(B)=sqrt(2gh_(B)(1-costheta_(B)))` ............iii `and (v_(0))/2(1+e)=sqrt(2gl_(B)(1-costheta_(B)))` `((2gl_(A)(1-costheta_(A)))/2(1+e) sqrt(2gl_(B)(1-costheta_(B)))` `implies (l_(B))/(l_(A))=((1+e)/2)^(2)`