Q. Four particles of mass 1 kg, 2 kg, 3 kg and 4 kg are placed at the corners $A,B,C$ and $D$ respectively of a square $ABCD$ of edge $X$-axis and edge $AD$ is taken along $Y$-axis, the co-ordinates of centre of mass in SI is
A) (1,1)
B) (5,7)
C) (0.5,0.7)
D) None of these
Explanation
(c) $x_{CM} = \frac{m_{A}x_{A} + m_{B}x_{B} + m_{C}x_{C} + m_{D}x_{D}}{m_{A} + m_{B} + m_{C} + m_{D}}$
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$= \frac{1 \times 0 + 2 \times 1 + 3 \times 1 + 4 \times 0}{1 + 2 + 3 + 4}$
$= \frac{2 + 3}{10} = \frac{1}{2} = 0.5$ m
Similarly, $y_{CM} = \frac{m_{A}y_{A} + m_{B}y_{B} + m_{C}y_{C} + m_{D}y_{D}}{m_{A} + m_{B} + m_{C} + m_{D}}$
$= \frac{1 \times 0 + 2 \times 0 + 3 \times 1 + 4 \times 1}{1 + 2 + 3 + 4}$
$= \frac{7}{10} = 0.7$ m
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.