Mass is distributed uniformly over a thin rectangular plate and p… - Vidyadip

MCQ

Mass is distributed uniformly over a thin rectangular plate and positions of two vertices are given by $(1, 3)$ and $(2, -4)$. What is the position of $3^{rd}$ vertex if centre of mass of the plate lies at the origin ?

A
$(1, -2)$
B
$(-2, 4)$
✓
$(-3, 1)$
D
$(1, 2)$

✓

Answer

Correct option: C.

$(-3, 1)$

c
$\left(\mathrm{x}_{\mathrm{CM}}, \mathrm{y}_{\mathrm{CM}}\right)=\left(\frac{\mathrm{x}_{1}+\mathrm{x}_{2}+\mathrm{x}_{3}}{3}, \frac{\mathrm{y}_{1}+\mathrm{y}_{2}+\mathrm{y}_{3}}{3}\right)$

$(0,0)=\left(\frac{1+2+x_{3}}{3}, \frac{3-4+y_{3}}{3}\right)$

$\left(\mathrm{x}_{3}, \mathrm{y}_{3}\right)=(-3,1)$

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