Answer to Question #96930 in Mechanics | Relativity for Mazhar

Question

The mass (in kg), position coordinates (in m) and velocity (in m s−1) of a system of three particles A, B and C are as follows: Particle Mass A B C 2.0 kg 1.0 kg 3.0 kg Position (0, 0) (2, 0) (1, 1) Velocity r 0 4.0ˆ j 2.0ˆ

Answer 1

Velocity of A = 0

Velocity of B = $4\hat{j}$

Velocity of C = $2\hat{i}$

coordinates of A,B and C = $(0,0),(2,0)\ and\ (1,1)\ respectively$

mass of A,B and C = 2kg, 1kg and 3kg respectively

Coordinates of center of mass -

$$x=\frac{m_1x_1+m_2x_2+m_3x_3}{m_1+m _2 +m_3 }=\frac{0+2+3}{6}=\frac{5}{6}$$

$$y=\frac{m_1y_1+m_2y_2+m_3y_3}{m_1+m _2 +m_3 }=\frac{0+0+3}{6}=\frac{1}{2}$$

Coordinate of center of mass =

$$(x,y)=(\frac{5}{6},\frac{1}{2})$$