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Question

Three point masses 1 kg,1.5 kg,2.5 kg are placed at the vertices of a triangle with sides 3 cm,4 cm and 5 cm as shown in the figure. The location of the centre of mass with respect to the 1 kg mass is:


A
0.6 cm to the right of 1 kg and 2 cm above 1 kg mass
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B
0.9 cm to the right of 1 kg and 2 cm above 1 kg mass
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C
0.9 cm to the left of 1 kg and 2 cm above 1 kg mass
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D
0.9 cm to the right of 1 kg and 1.5 cm above 1 kg mass
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Solution

The correct option is B 0.9 cm to the right of 1 kg and 2 cm above 1 kg mass
Assume 1 kg mass as origin.


As we know,
Xcm=m1×x1+m2×x2+m3×x3m1+m2+m3
Xcm=1×0+1.5×3+2.5×05=0.9 cm
and,
Ycm=m1×y1+m2×y2+m3×y3m1+m2+m3
Ycm=1×0+1.5×0+2.5×45=2 cm
Hence, center of mass of the system will be 0.9 cm to the right of 1 kg and 2 cm above 1 kg mass.

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