Question

The velocity vectors of three particles of masses 1 kg, 2 kg and 3 kg are respectively (1, 2, 3), (3, 4, 5) and (6, 7, 8). The velocity vectors are in m/s. Find the velocity vector of centre of mass of this system of particles.

Answer 1

Answer:

to find velocity vector of com for those system of particles jst calculate the velocity of com in the three given directions

Answer 2

Answer:

$(\frac{25}{6},\frac{31}6},\frac{37}{6})$

Explanation:

In this question,

We have been given that,

Velocity vector of 1 k.g body = (1,2,3) = $\hat{i}\ +\ 2\hat{j}\ +\ 3\hat{k}$

Velocity vector of 2 k.g body = (3,4,5) =$3\hat{i}\ +\4\hat{j}\ +\  5\hat{k}$

Velocity vector of 5k.g body = (6,7,8) = $6\hat{i}\ +\ 7\hat{j}\ +\ 8\hat{k}$

We need to find the velocity vector of centre of mass of this system of particles.

Velocity of centre of mass for this system of Particles is given by = $\frac{\sum{m_{i}v__{i}}}{Total Mass}$    where i = {1,2,3}

Velocity of centre of mass for this system of particles = $\frac{1(\hat{i}+2\hat{j}+3\hat{k})+2(3\hat{i}+4\hat{j}+5\hat{k})+3(6\hat{i}+7\hat{j}+8\hat{k})}{1+2+3}$

Velocity of centre of mass for this system of particles = $\frac{25\hat{i}\ +\ 31\hat{j}\ +\ 37\hat{k}}{6}$

Therefore, Velocity of centre of mass is = ($\frac{25}{6},\frac{31}{6},\frac{37}{6}$)