Q 11-06-077JEE MainJEE Main 2024 (1 Feb, Shift 1)Easy
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 the point of intersection of these two sides as origin, the magnitude of the position vector of the centre of mass of the system is $\dfrac{4\sqrt2}{x}$, where the value of $x$ is ______.
Numerical value type. Enter your answer.
Answer: 3
The spheres are at $(0,0)$, $(4,0)$ and $(0,4)$. With equal masses,
$$x_{cm} = \frac{0 + 4 + 0}{3} = \frac43,\qquad y_{cm} = \frac43$$
$$|\vec r_{cm}| = \sqrt{\left(\tfrac43\right)^2 + \left(\tfrac43\right)^2} = \frac{4\sqrt2}{3} \Rightarrow x = 3$$
Solution by Sreeraj P, M.Sc Physics