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» <html><body><p></p>Solution :Velocity of `A` just before collision <br/> `v_(0)=sqrt(2gl_(A)(1-costheta_(A))`………..i<br/> Collision of `A` and `B` <br/> Using C.O.L.M. , `m.v_(0)+0=mv_(A)+mv_(B)` <br/> `v_(A)+v_(B)=v_(0)`……ii <br/> Using <a href="https://interviewquestions.tuteehub.com/tag/newton-11212" style="font-weight:bold;" target="_blank" title="Click to know more about NEWTON">NEWTON</a>'s restitution law <br/> `v_(B)-v_(A)=v_(0)` <br/> `v_(B)-v_(A)=ev_(0)`………ii <br/> Solving <a href="https://interviewquestions.tuteehub.com/tag/eqn-973463" style="font-weight:bold;" target="_blank" title="Click to know more about EQN">EQN</a> i and ii `v_(A)=(v_(0))/2(1-e)` and `v_(B)=(v_(0))/2(1+e)` <br/> As `B` swings angle `thetaB`, hence <br/> `v_(B)=sqrt(2gh_(B)(1-costheta_(B)))` ............iii <br/> `and (v_(0))/2(1+e)=sqrt(2gl_(B)(1-costheta_(B)))` <br/> `((2gl_(A)(1-costheta_(A)))/2(1+e) sqrt(2gl_(B)(1-costheta_(B)))` <br/> `implies (l_(B))/(l_(A))=((1+e)/2)^(2)`</body></html>