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Question

From the uniform disc of radius R, an equilateral triangle of side 3R is cut as shown in the figure. The new position of the centre of mass is :
1021542_156c952832514e8a843532d3a75bc41e.png

A
(0,0)
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B
(0,R)
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C
(0,3R2)
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D
None of these
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Solution

The correct option is A (0,0)
Let σ is mass per unit area.
Mass of disc M1=σπR2 and mass of equilateral triangle M2=σ334R2,

Centre of mass (COM) of disc is at centre of the disc. COM of equilateral triangle is centroid of triangle.

COM in direction of x axis , x=M1x1+M2x2M1+M2

COM in direction of y axis , y=M1y1+M2y2M1+M2

A new position of COM from a center of the disc.

In direction x axis, x=M1×0M2×0M1+M2=0

In direction y axis, y=M1×0M2×0M1+M2=0\Hence, new COM =(0,0)

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