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Three identical spheres at the corners of a right-angled isosceles triangle: position of the centre of mass

The same question, asked 2 times: 25 Jul 2022*, 1 Feb 2024. Every wording below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    25 Jul 2022

    112
    Three identical spheres each of mass MM are placed at the corners of a right -angled triangle with mutually perpendicular sides equal to 3 m3\text{ }m each. Taking point of intersection of mutually perpendicular sides as origin, the magnitude of position vector of centre of mass of the system will be xm\sqrt{x}m. The value of xx is

  2. Question 2

    1 Feb 2024

    26
    Three identical spheres each of mass 2M2M are placed at the corners of a right-angled triangle with mutually perpendicular sides equal to 4 m4\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 42x\frac{4\sqrt{2}}{x}, where the value of xx is _____