Three identical spheres each of mass 2M are placed at the corners of… | JEE Main 2024 (1 Feb, Shift 1)

Q8JEE Main 2024 · 1 FEB · SHIFT 1Easy

Centre of Mass of Discrete Particles

Three identical spheres each of mass $2M$ are placed at the corners of a right angled triangle with mutually perpendicular sides equal to $4\text{ m}$ each. Taking point of intersection of these two sides as origin, the magnitude of position vector of the centre of mass of the system is $\frac{4\sqrt{2}}{x}$ , where the value of $x$ is ___________.

Numerical answer type. Work it out, then open the answer.

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Answer: 3

Masses $2M$ at $(0,0)$ , $(4,0)$ and $(0,4)$ m.
$x_{cm} = \frac{4}{3}$ m, $y_{cm} = \frac{4}{3}$ m
$|\vec{r}_{cm}| = \frac{4}{3}\sqrt{2} = \frac{4\sqrt{2}}{3}$
So $x = 3$ .

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Centre of Mass of Discrete Particles question from JEE Main 2024 (1 Feb, Shift 1)

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