Three particles of masses 1 kg, (3)/(2) kg, and 2 kg are located at the vertices of an equila

step 1 In this question we have given three particles of masses 1 kilogram 3 kilogram and 2 kilograms a

Three particles of masses 1 kg, (3)/(2) kg, and 2 kg are...

Three particles of masses $1 \mathrm{~kg}, \frac{3}{2} \mathrm{~kg}$, and $2 \mathrm{~kg}$ are located at the vertices of an equilateral triangle of side $a$. The $x_{1} y$ coordinates of the centre of mass are (a) $\left(\frac{5 a}{9}, \frac{2 a}{3 \sqrt{3}}\right)$ (b) $\left(\frac{2 a}{3 \sqrt{3}}, \frac{5 a}{9}\right)$ (c) $\left(\frac{5 a}{9}, \frac{2 a}{\sqrt{3}}\right)$ (d) $\left(\frac{2 a}{\sqrt{3}}, \frac{5 a}{9}\right)$

Three particles of masses $1 \mathrm{~kg}, \frac{3}{2} \mathrm{~kg}$, and $2 \mathrm{~kg}$ are located at the vertices of an equilateral triangle of side $a$. The $x_{1} y$ coordinates of the centre of mass
are
(a) $\left(\frac{5 a}{9}, \frac{2 a}{3 \sqrt{3}}\right)$
(b) $\left(\frac{2 a}{3 \sqrt{3}}, \frac{5 a}{9}\right)$
(c) $\left(\frac{5 a}{9}, \frac{2 a}{\sqrt{3}}\right)$
(d) $\left(\frac{2 a}{\sqrt{3}}, \frac{5 a}{9}\right)$

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Key Concepts

Center of Mass

The center of mass is a point representing the average location of all the mass in a system. It is calculated by taking the weighted average of the positions of all the individual masses. This concept is essential in mechanics, as it simplifies the analysis of motion, determining how forces affect the overall system.

Coordinate System in Mechanics

Utilizing a coordinate system is fundamental in physics for representing the positions of particles in space. By assigning coordinates to each mass, one can mathematically calculate properties like the center of mass by resolving the system into its component directions.

Geometric Properties of an Equilateral Triangle

An equilateral triangle has equal sides and equal angles of 60° each. Its symmetry properties are advantageous in solving problems involving spatial arrangements of particles, as they allow for a simplified and systematic assignment of coordinates.

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