A uniform rod of mass m and length l rests on a smooth horizontal surface. One of the ends of the rod is struck in a horizontal direction at right angles to the rod. As a result the rod obtains velocity v_(0). Find the force with which one-half of the rod will act ont he other in the process of motion.

A uniform rod of mass m and length l rests on a smooth horizontal surf

1.	A uniform rod of mass m and length l rests on a smooth horizontal surface. One of the ends of the rod is struck in a horizontal direction at right angles to the rod. As a result the rod obtains velocity v_(0). Find the force with which one-half of the rod will act ont he other in the process of motion.
Answer» Solution : LET `J` be the linear impulse applied at B and `OMEGA` and angular speed of rod `J=mv_(0)`..(i) ,BRGT `J((l)/(2))=(ml^(2))/(12).omega`.(ii) solving these two equations `omega=(6v_(0))/(l)` Linear speed of D (mid-point of CB) relative C `v=omega((l)/(4))=(3)/(2)v_(0)` `therefore` force exerted by upper half on the LOWER half `F=(((m)/(2))v^(2))/(((l)/(4)))` substituting `v=(3)/(2)v_(0)`, we get `F=(9)/(2)(mv_(0)^(2))/(l)`