Three particles of masses 2kg,3kg & 4kg are placed at the three vertices of a right angled triangle with sides 3cm,4cm & 5cm 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 2kg and writing the x and y coordinates of masses in the table given below:
massx(cm)y(cm)m1=2kg00m2=3kg03m3=4kg40
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