A meter stick weighing 240 g is pivoted at its upper end in such a way that it can freely rotate in a vertical plane through this end (figure 10-E12). A particle of mass 100 g is attached to the upper end of the stick through a light string of length 1 m. Initially, the rod is kept vertical and the string horizontal when the system is released from rest. The particle collides with the lower end of the stick and sticks there. Find the maximum angle through which the stick will rise.



Given:


Weight of the stick = 240g


Mass of the particle= 100g


Length of the string= 1m


Length of the stick= 1m


Let the angular speed of the system =


Rotational energy of the string is given as





The angular momentum of the system before the strike = Angular momentum of the string-particle + Angular momentum of the rod


=I+0=I


= 0.10


Let the angular speed of the rod after the strike be '.


Now the angular momentum = I''




Comparing (1) and (2), as angular momentum is conserved




Kinetic energy=


Substituting the value of I’ and in the above equation we get, Kinetic energy= 0.055g


Change in potential energy of the system at angle θ after the strike





Comparing equation (1) and (2)




1