Question

The figure below shows a three-particle system, with masses m1 = 2.3 kg, m2 = 4.0 kg, and m3 = 9.0 kg. N (a) What are the coordinates of the center of mass? m (x-coordinate) m (y-coordinate) (b) What happens to the center of mass as the mass of the topmost particle is gradually increased? The center of mass shifts toward the particle on the right. The center of mass shifts toward the particle on the left. The center of mass shifts toward the topmost particle.

Answer 1

(a) X- coordinate of center of mass = (m1*x1 + m2*x2 + m3*x3) / (m1 + m2 + m3)

= (2.3*0 + 4.0*2.0 + 9.0*1.0) / (2.3+4.0+9.0)

= (0 + 8.0 + 9.0) / 15.3

= 1.11 m

Y- coordinate of center of mass = (m1*y1 + m2*y2 + m3*y3) / (m1 + m2 + m3)

= (2.3*0 + 4.0*1.0 + 9.0*2.0) / (2.3+4.0+9.0)

= (0 + 4.0 + 18.0) / 15.3

= 1.44 m (Answer)

(b) Third option, the center of mass shifts toward the topmost particle' is the correct answer.

Explanation -

when, m3 will be larger, coordinates of m3 will be considerable in respect to the coordinates of m1 and m2. Therefore, coordinate of center of mass will move towards m3.