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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


A
a5(^i^j)
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B
a5(^i+^j)
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C
Zero
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D
a(^i+^j)
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Solution

The correct option is A a5(^i^j)

aA=a^i
aB=a^j
aC=a^i
aD=a^j
acm=maaa+mbab+mcac+mdadma+mb+mc+md
acm=ma^i+2maj+3ma^i4ma^j10m
=2ma^i2ma^j10m
=a5^ia5^j
=a5(^i^j).

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