Center of Mass (a) You are given the velocities of five particles as shown below in Fig. 3. Figure 3 Calculate the velocity of the center of mass (CM) of the system of particles. (b) Find the centre of mass of a uniform plate (shown in Fig. 4) having semicircular inner and outer boundaries of radii R1, and R2.
![A 50 kg child stands on the edge of a stationary thin rod of length 5.0 m and mass M = 100 kg, free to rotate around its center of mass O. The child catches a ball of mass 2.0 kg thrown by a friend. Just before the ball is caught, the ball has a horizontal velocity of magnitude 30 ms−1, at angle θ = π/4 with a rod, as shown in Fig. 4 (a) What is the angular speed of the thin rod just after the ball is caught? (b) What is the mechanical energy of the child after the ball has been caught? [6 marks] (c) With what horizontal velocity, at an angle ϕ = π/6 with respect to the rod, has the boy to throw away the ball such that after the launch he will stay at rest? [7 marks]](https://www.doubtrix.com/uploads/editor/9895436237ysrDMhQJnq.png)
