NEET 2024 Model Paper

Let the centres $A$, $B$ and $C$ lie on the $x$-axis, with the centre $A$ at the origin.Since the spheres are identical and touch each other, the distance between the centres of two adjacent spheres equals the sum of their radii: $AB = BC = R + R = 2R$.Therefore the positions of the three centres are:$x_A = 0,\quad x_B = 2R,\quad x_C = 4R$.All three spheres have the same mass $m$, so the centre of mass of the system is$$x_{cm} = \frac{m x_A + m x_B + m x_C}{m + m + m} = \frac{m(0) + m(2R) + m(4R)}{3m} = \frac{6R}{3} = 2R.$$Thus the centre of mass is at a distance $2R$ from the centre $A$.Hence the correct option is $2R$.