Q.

An object comprises of a uniform ring of radius R and its uniform chord AB (not necessarily made of the same material) as shown. Which of the following cannot be the centre of mass of the object?

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a

(R/3, R/3)

b

(R/√2, R/√2)

c

(R/4, R/4)

d

None of the above

answer is B.

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Detailed Solution

The centre of mass of the object must lie on the line segment joining (0, 0) and . (R/2, R/2). Co-ordinates of centre of mass of rod are (R/2, R/2) and Co-ordinates of centre of mass of ring are (0, 0). So the centre of mass of the object must lie on the line joining (0, 0) and . (R/2, R/2). Hence xc < R/2 and yc < R/2. Since R/√2 > R/2, option (2) is right.
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