Q. Centre of mass of 3 particles $10\ kg,\ 20\ kg$ and $30\ kg$ is at (0, 0, 0). Where should a particle of mass $40kg$ be placed so that the combination centre of mass will be at (3, 3, 3)
A) (0,0,0)
B) (7.5, 7.5, 7.5)
C) (1, 2, 3)
D) (4, 4, 4)
Explanation
(b) $X = \frac{m_{1}x_{1} + m_{2}x_{2} + m_{3}x_{3} + m_{4}x_{4}}{m_{1} + m_{2} + m_{3} + m_{4}}$
$X = \frac{0 + 40\ x_{4}}{100} \Rightarrow 3 = \frac{40\ x_{4}}{100}$
$x_{4} = \frac{300}{40} = 7.5$
Similarly $y_{4} = 7.5$ and $z_{4} = 7.5$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.