Q63 of 149 Page 195

Two small balls A and B, each of mass m, are joined rigidly to the ends of a light rod of length L (figure 10-E10). The system translates on a frictionless horizontal surface with a velocity in a direction perpendicular to the rod. A particle P of mass m kept at rest on the surface sticks to the ball A as the ball collides with it. Find

(a) the linear speeds of the balls A and B after the collision, (b) the velocity of the center of mass C of the system A + B + P and (c) the angular speed of the system about C after the collision.



[Hint: The light rod will exert a force on the ball B only along its length.]



Given:


Mass of each ball = m


Length of the rod= L


Velocity of the system=


(a) collision pf the particle P with the ball A will not affect the velocity of the ball because the force exerted by the rod is along the length


Velocity of B =


Using the law of conservation of linear momentum, we get,




Velocity of ball A=


(b) consider the system of three bodies as one single system


Not external force is acting on the system


Hence,





(c) velocity of particle P and the ball A with respect to the center of the mass



Velocity of ball B with respect to center of the mass=


Distance of the particle P and ball A from the center of mass =


Distance of ball B from the center of mass=


For angular speed






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