An object comprises a uniform ring of radius | vedclass

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(D) The centre of mass $(C.M.)$ of the ring is at the origin $(0, 0)$.The centre of mass of the chord $AB$ lies at its midpoint,which is $(R/2, R/2)$.

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both $(B)$ and $(C)$

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(D) The centre of mass $(C.M.)$ of the ring is at the origin $(0, 0)$.The centre of mass of the chord $AB$ lies at its midpoint,which is $(R/2, R/2)$.The $C.M.$ of the combined system must lie on the line segment connecting the $C.M.$ of the ring and the $C.M.$ of the chord.This line segment is the line $y = x$ for $0 \le x \le R/2$.Therefore,the $C.M.$ of the system must have coordinates $(x, x)$ where $0 \le x \le R/2$.Option $(A)$ $(R/3, R/3)$ satisfies this condition.Option $(B)$ $(R/3, R/2)$ does not satisfy $x = y$.Option $(C)$ $(R/\sqrt{2}, R/\sqrt{2})$ has $x = R/\sqrt{2} \approx 0.707R$,which is greater than $R/2 = 0.5R$,so it lies outside the possible range.Thus,both $(B)$ and $(C)$ cannot be the centre of mass.

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

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