Passage: A uniform circular disk of radius 0.2 m and mass 1 kg is pivoted at its top point C such that it can rotate freely around C in the XY plane, as shown in the figure. Initially, when the disk is at rest, a particle of mass 20 g, travelling along negative x direction in the XY plane with speed 100 ms ⁻¹ , hits the circumference of the disk at a point P . After collision the particle moves along negative y direc

Step-by-step solution

Let the center of the uniform circular disk be the origin O(0,0) . The disk is pivoted at its top point C(0, R) . Radius of disk R = 0.2 m, Mass M = 1 kg. Mass of particle m = 20 g = 0.02 kg. Initial velocity of particle v _i = -100 i ms ⁻¹ . Final velocity of particle v _f = -90 j ms ⁻¹ . The particle hits the disk at point P . From the figure, the line OP makes an angle of 45^ with the negative y-axis. Coordinates of P with respect to O are (R 45^ , -R 45^ ) . Position vector of P with respect to the pivot C is: