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Question

Three particles of masses 2 kg,3 kg & 4 kg are placed at the three vertices of a right angled triangle with sides 3 cm,4 cm & 5 cm as shown in the figure. What will be the coordinates of centre of mass of the system of particles ?


A
(169,2)
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B
(1,916)
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C
(169,1)
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D
(1,169)
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Solution

The correct option is C (169,1)
Assigning origin at mass 2 kg and writing the x and y coordinates of masses in the table given below:


massx(cm)y(cm)m1=2 kg00m2=3 kg03m3=4 kg40

Applying the formula for the coordinates of CM of system:
xCM=m1x1+m2x2+m3x3m1+m2+m3=(2×0)+(3×0)+(4×4)2+3+4
xCM=169
Similarly
yCM=m1y1+m2y2+m3y3m1+m2+m3=(2×0)+(3×3)+(4×0)2+3+4=99=1

(xCM, yCM)=(169,1)

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