Question

The center of mass of a system of three particles of masses $1g,2g$ and $3g$ is taken as the origin of a coordinate system. The position vector of a fourth particle of mass $4g$ such that the center of mass of the four particle system lies t the point $(1,2,3,)$ is $\alpha \left(\hat{i}+2\hat{j}+3\hat{k}\right)$, where $\alpha$ is a constant. The value of $\alpha$ is: -

• A. $\frac{10}{3}$
• B. $\frac{5}{2}$
• C. $\frac{1}{2}$
• D. $\frac{2}{5}$

Answer 1

The correct option is B $\frac{5}{2}$

COM of y coordinate

$=\frac{[m_1\times y_1+m_2\times y_2+m_3\times y_3+m_4\times y_4]}{m_1+m_2+m_3+m_4}$

but the $1^{st}$ $3$ terms in the numerator is equal to zero

hence

COM$=4\times \frac{2a}{10}=2$

$a=\frac{5}{2}$ required answer.