Question

Consider the mass distribution of 3 kg at $(0,0)$, 4 kg at $(0,4)$ & 5 kg at $(3,0)$. Where should a fourth mass of 8 kg be placed, so that centre of mass of complete arrangement will be at $(0,0)$?

• A. $(\frac{-15}{8},2)$
• B. $(\frac{-15}{8},-2)$
• C. $(\frac{-7}{15},-3)$
• D. $(\frac{-6}{15},-4)$

Answer 1

The correct option is B $(\frac{-15}{8},-2)$

Let 8 kg mass be placed at $(x,y)$.

$X_{CM}=\frac{\sum mx}{\sum m}=0,\sum mx=3\left(0\right)+4\left(0\right)+5\left(3\right)+8\left(x\right)=015+8x=0x=\frac{-15}{8}{Y}_{CM}=\frac{\sum my}{\sum m}=0,\sum my=03\left(0\right)+4\left(4\right)+5\left(0\right)+8y=0y=\frac{-16}{8}=-2\{\frac{-15}{8},-2\}$