Three identical spheres of mass M are at the corners of a right-angled triangle with mutually perpendicular sides of 2 m, as shown. Taking their intersection as origin, find the position vector of the centre of mass.

Question

G1 Physics · Accepted Answer

Step 1: Their centres are at (0,0), (2,0) and (0,2) m. Step 2: Therefore centre-of-mass x-coordinate=(0+2+0)/3=2/3 m and centre-of-mass y-coordinate=(0+0+2)/3=2/3 m, so centre-of-mass position vector=(2/3)(i+j) m. Final answer: C — (2/3)(i+j) m.