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Question

Three particles, each of mass 'm', are placed at the corners of a right angled triangle as shown in Fig. If OA = a and OB = b, the position vector of the centre of mass is (here i and j are unit vectors along x and y axes respectively).


A

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B
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C
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D
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Solution

The correct option is A

The (x, y) co-ordinates of the masses at 0, A and B respectively are (refer to fig. 5.4)
(x1=0,y1=0),(x2=a,y2=0)and(x3=0,y3=b)
The (x,y) co - ordinates of the centre of the centre of mass are xCM=m1x1+m2x2+m3x3m1+m2+m3=m×0+m×a+m×0m+m+m=a3
yCM=m1y1+m2y2+m3y3m1+m2+m3=m×0+m×0+m×bm+m+m=b3
The position vector of the centre of mass is xCMi+yCMj
=a3i+b3j=13(ai+bj), which is choice (a).

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