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Question

Three identical circular plates of radius R each are placed on a horizontal surface touching one another as shown in the figure. The y coordinate of the center of mass of the system is [Consider A to be at the origin]


A
R3
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B
R3
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C
3R
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D
R
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Solution

The correct option is B R3

Here,
PC2=AC2AP2
PC=4R2R2
PC=3R
Then, coordinates of A is (0,0)
coordinates of B is (2R,0)
coordinates of C is (R,3R).

xcom of system =m1x1+m2x2+m3x3m1+m2+m3
xcom=m×0+m×2R+m×Rm+m+m=R

ycom=m1y1+m2y2+m3y3m1+m2+m3=m×0+m×0+m×3Rm+m+m
ycom=3mR3m=R3
Hence, the coordinates of the COM of the system are (R,R3)

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