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Question

(C) For a uniform rectangular plate,the centre of mass coincides with the geometric centre of the rectangle. However,the problem asks for the $3^{rd}$

Vedclass · Accepted Answer

$(-3, 1)$

Vedclass · Answer

(C) For a uniform rectangular plate,the centre of mass coincides with the geometric centre of the rectangle. However,the problem asks for the $3^{rd}$ vertex given the centre of mass is at the origin $(0, 0)$.Assuming the plate is a triangle defined by three vertices $(x_1, y_1)$,$(x_2, y_2)$,and $(x_3, y_3)$,the centre of mass is given by:$(x_{CM}, y_{CM}) = \left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right)$Given $(x_1, y_1) = (1, 3)$,$(x_2, y_2) = (2, -4)$,and $(x_{CM}, y_{CM}) = (0, 0)$:$0 = \frac{1 + 2 + x_3}{3} \implies 3 + x_3 = 0 \implies x_3 = -3$$0 = \frac{3 - 4 + y_3}{3} \implies -1 + y_3 = 0 \implies y_3 = 1$Therefore,the position of the $3^{rd}$ vertex is $(-3, 1)$.

Column-$I$	Column-$II$
$(1)$ $\frac{{{m_1}{m_2}}}{{{m_1} + {m_2}}}$	$(a)$ Reduced mass of a two-particle system
$(2)$ $\frac{{{r_1} + {r_2}}}{2}$	$(b)$ Position vector of the center of mass for a system of two equal masses

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

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