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Question

A square of edge d and a circular disc of diameter d are placed touching each other at the midpoint of an edge of the plate as shown in the figure.The centre of mass of the combination assuming same mass per unit area for the two plates from the centre of the disk is the
1163776_0cacbaedbb5347e5a77a1ec7f58f340c.png

A
4d4+π towards right
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B
4d4+π towards left
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C
4d4π towards right
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D
4d4π towards left
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Solution

The correct option is A 4d4+π towards right
Let m be the mass per unit area.

Mass of the square plate =M1=d2m

Mass of the circular disc =M2=πd24m

Let the centre of the circular disc be the origin of the system.

Position of centre of mass

=(d2md+π(d2/4)m×0d2m+π(d2/4)m,0+0M1+M2)=⎜ ⎜ ⎜ ⎜d3md2m(1+π4),0⎟ ⎟ ⎟ ⎟=(4dπ+4,0)

The new centre of mass is (4dπ+4) right of the centre of circular disc.

2057616_1163776_ans_2b078ed8740a4a91baf5b1ec7fc7da48.png

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