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Question

Four particles of masses m1=2m, m2=4m, m3=m and m4 respectively are placed at the four corners of a square. What should be the value of mass m4 so that the centre of mass of the system of particles lies at the centre of square?


A
m
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B
2m
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C
4m
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D
6m
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Solution

The correct option is C 4m

Considering a square with side a and assigning origin (0,0) at mass m1 .

The x and y coordinates of all masses can be written as :
m1=2m,(0,0)
m2=4m,(a,0)
m3=m,(a,a)
m4=m4,(0,a)

COM of system of particles should be at the centre of the square. Hence coordinates of COM is represented by (xCOM, yCOM)=(a2,a2)....(i)

Applying the formula and equating the x and y coordinates of COM from Eq. (i)

xCOM=m1x1+m2x2+m3x3+m4x4m1+m2+m3+m4

a2=0+4ma+ma+02m+4m+m+m4=5ma(7m+m4)...(ii)

Simillarly, yCOM=m1y1+m2y2+m3y3+m4y4m1+m2+m3+m4

a2=0+0+ma+m4a7m+m4=(m+m4)a7m+m4.....(iii)

Equating Eq. (ii) & (iii):
5ma=(m+m4)a
m4=5mm=4m
m4=4m


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