First slide

Location of centre on mass for multiple point masses

Question

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?

Moderate

A

(R/3, R/3)
B

(R/√2, R/√2)
C

(R/4, R/4)
D

None of the above

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 x_c < R/2 and y_c < R/2. Since R/√2 > R/2, option (2) is right.

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