Two bodies of mass 1 kg and 3 kg have posit | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Given:$m_1 = 1 \ kg$,$\vec{r}_1 = \hat{i} + 2\hat{j} + \hat{k}$$m_2 = 3 \ kg$,$\vec{r}_2 = -3\hat{i} - 2\hat{j} + \hat{k}$The position vector of t

Vedclass · Accepted Answer

$-2\hat{i} - \hat{j} + \hat{k}$

Vedclass · Answer

(A) Given:$m_1 = 1 \ kg$,$\vec{r}_1 = \hat{i} + 2\hat{j} + \hat{k}$$m_2 = 3 \ kg$,$\vec{r}_2 = -3\hat{i} - 2\hat{j} + \hat{k}$The position vector of the centre of mass is given by:$\vec{r}_{CM} = \frac{m_1\vec{r}_1 + m_2\vec{r}_2}{m_1 + m_2}$Substituting the values:$\vec{r}_{CM} = \frac{1(\hat{i} + 2\hat{j} + \hat{k}) + 3(-3\hat{i} - 2\hat{j} + \hat{k})}{1 + 3}$$\vec{r}_{CM} = \frac{\hat{i} + 2\hat{j} + \hat{k} - 9\hat{i} - 6\hat{j} + 3\hat{k}}{4}$$\vec{r}_{CM} = \frac{-8\hat{i} - 4\hat{j} + 4\hat{k}}{4}$$\vec{r}_{CM} = -2\hat{i} - \hat{j} + \hat{k}$

Two bodies of mass $1 \ kg$ and $3 \ kg$ have position vectors $\hat{i} + 2\hat{j} + \hat{k}$ and $-3\hat{i} - 2\hat{j} + \hat{k}$,respectively. The centre of mass of this system has a position vector:

Similar Questions

Where is the centre of mass of two isolated particles of equal mass located?

$A$ uniform thin rod of length $L$ and mass $M$ is placed along the $x$-axis with one end at the origin. Find the position of the centre of mass of the rod.

Four identical spheres each of mass $m$ are placed at the corners of a square of side $2 \, m$. Taking the point of intersection of the diagonals as the origin,the coordinates of the centre of mass are

Four bodies of equal mass start moving with the same speed as shown in the figure. In which of the following combinations will the centre of mass remain at the origin?

Three masses are placed on the $x-$axis: $300 \, g$ at the origin,$500 \, g$ at $x = 40 \, cm$ and $400 \, g$ at $x = 70 \, cm$. The distance of the centre of mass from the origin is ....... $cm$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module