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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

Question

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Solution

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 Rcm \vec{R}_{cm} for a system of particles is given by the formula:

Rcm=m1r1+m2r2m1+m2 \vec{R}_{cm} = \frac{m_1 \vec{r_1} + m_2 \vec{r_2}}{m_1 + m_2}

Where:

  • m1 m_1 and m2 m_2 are the masses of the bodies.
  • r1 \vec{r_1} and r2 \vec{r_2} are the position vectors of the bodies.

3. Analysis and Detail

Let's denote:

  • m1=4kg m_1 = 4 \, \text{kg}
  • m2=5kg m_2 = 5 \, \text{kg}
  • Let r1=r1 \vec{r_1} = \vec{r_1} be the position vector of the first body.
  • Let r2=r2 \vec{r_2} = \vec{r_2} be the position vector of the second body.

Substituting these into the formula, we get:

Rcm=4r1+5r24+5 \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 r1 \vec{r_1} and r2 \vec{r_2} . Once those values are provided, substitute them into the equation to find Rcm \vec{R}_{cm} .

Final Answer

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

Rcm=4r1+5r29 \vec{R}_{cm} = \frac{4 \vec{r_1} + 5 \vec{r_2}}{9}

Please replace r1 \vec{r_1} and r2 \vec{r_2} with their respective values to calculate the exact position vector of the center of mass.

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