Question

Three identical spheres each of mass 1kg are placed touching each other with the centers on a straight line.The centers are marked as A,B,C respectively.The distance of the centre of mass from A is

Answer 1

Refer to the attachment , it will clear your half of the doubt.

Now according to the question there are many given circumstances.

Here we see the center of mass of the system lies on the center of sphere B

So we know the formula ,

Center of mass of the given system

x = [ $M_ax_a$ + $M_bx_b$ + $M_cx_c$ ] / (M + M + M)

x = [ M( 0 ) + M( AB ) + M( AC ) ] /  3 M

x = ( AB + AC ) / 3

Hence the distance form the centre of mass from A is (AB +AC)/3 .

Hope it helps :-)