In which of the following cases, the centre of mass of rod may be its centre ?
(1) The linear mass density increases continuously from left to right.
(2) The linear mass density decreases continuouly from let to right.
(3) The linear mass density decreases from left to right up to centre and then increases.
(4) The linear mass density increases form left to right upto a certain point (may not be the centre) and the decreases from the point till the end.

Options

A. 1,2,3,4
B. 3,4
C. only 3
D. None of the above

Answer

B

Explanation

(1) The centre of mass is towards right of the centre of the rod as the rod is heavier towards right.
(2) Similarly the COM is towards left of the centre of the rod.
(3) ,(4) The COM may lie at the centre of the rod in these cases.