Two bodies of masses 4 kg and 5 kg are kept at fixed locations having position vectorsrespectively. The position vector of centre of mass of this system is

1. Break Down the Problem

We need to find the position vector of the center of mass of a system consisting of two bodies with given masses and their respective position vectors.

2. Relevant Concepts

The position vector of the center of mass $\vec{R}_{cm}$ for a system of particles is given by the formula:

$\vec{R}_{cm} = \frac{m_1 \vec{r_1} + m_2 \vec{r_2}}{m_1 + m_2}$

Where:

• $m_1$ and $m_2$ are the masses of the bodies.
• $\vec{r_1}$ and $\vec{r_2}$ are the position vectors of the bodies.

3. Analysis and Detail

Let's denote:

• $m_1 = 4 \, \text{kg}$
• $m_2 = 5 \, \text{kg}$
• Let $\vec{r_1} = \vec{r_1}$ be the position vector of the first body.
• Let $\vec{r_2} = \vec{r_2}$ be the position vector of the second body.

Substituting these into the formula, we get:

$\vec{R}_{cm} = \frac{4 \vec{r_1} + 5 \vec{r_2}}{4 + 5}$

4. Verify and Summarize

To find the center of mass, you need the specific values for $\vec{r_1}$ and $\vec{r_2}$. Once those values are provided, substitute them into the equation to find $\vec{R}_{cm}$.

Final Answer

The position vector of the center of mass is given by:

$\vec{R}_{cm} = \frac{4 \vec{r_1} + 5 \vec{r_2}}{9}$

Please replace $\vec{r_1}$ and $\vec{r_2}$ with their respective values to calculate the exact position vector of the center of mass.