Calculation of Center of Mass: Practice Problem & Solution
Two bodies of mass $1text{ kg}$ and $3text{ kg}$ have position vectors $\hat{i} + 2\hat{j} + \hat{k}$ and $-3\hat{i} - 2\hat{j} + \hat{k}$, respectively. The center of mass of this system has a position vector: (2009)
Solution Explained:
To solve this problem, we apply the core principles of Calculation of Center of Mass. Understanding the underlying formula is key to arriving at the correct answer below:
Concept: Center of mass position vector formula. Formula: $\vec{r}_{cm} = \frac{m_1\vec{r}_1 + m_2\vec{r}_2}{m_1 + m_2}$. Solution: Substituting the given masses and position vectors yields $-2\hat{i} - \hat{j} + \hat{k}$.
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