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# Two uniform rods A and B of Lengths 5 m and 3 m are placed end to end. If their linear densities are $3\;kg/m$ and $2\;kg/m$, the position of their centre of mass from their interface is

a) 19/14 m on the side of the heavier rod. b) 8/7 m on the side of higheir rod. c) 2 m on the side of heavior rod. d) 2 m on the side of lighter rod.

We can consider the mass of each rod to be at COM
If origin is the interface
Then $X_{com}= \large\frac{15 \times (-2.5)+6 \times 1.5}{21}$
$\qquad=-\large\frac{28.5}{21}$
$\qquad=-\frac{19}{14}$
edited Jun 16, 2014