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Question:

Four particles A, B, C, and D with masses mA=m, mB=2m, mC=3m, and mD=4m are at the corners of a square. They have accelerations of equal magnitude with directions as shown. The acceleration of the centre of mass of the particles is

a5(i^+j^)

a5(i^-j^)

Zero

a(i^+j^)

Solution:

Correct option is A.
a5(i^-j^)
a→A = -ai
a→B = aj
a→C = ai
a→D = -aj
a→cm = (ma→a + mb→b + mc→c + md→d)/(ma + mb + mc + md)
a→cm = (-mai + 2maj + 3mai - 4maj)/10m = (2mai - 2maj)/10m = a5i - a5j = a5(i - j).