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Question
In which of the following cases the centre of mass of a rod is certainly not at its centre?
(a) the density continuously increases from left to right
(b) the density continuously decreases from left to right
(c) the density decreases from left to right upto the centre and then increases
(d) the density increases from left to right upto the centre and then decreases.
Solution
(a) the density continuously increases from left to right
(b) the density continuously decreases from left to right
As the density continuously increases/decreases from left to right, there will be difference in the masses of rod that lie on either sides of the centre of mass. Thus, the centre of mass of a rod in such a case will certainly not be at its centre.
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