Question

In each situation of column I a mass distribution is given and information regarding $x$ and $y$ coordinate of centre of mass is given in column II. Match the figures in column I with corresponding information of centre of mass in column II

Answer 1

A:
$x_{cm}<0$ since the rod having density $3\lambda$ is on the -ve x-axis and the rod having density $\lambda$ is on the +ve x-axis
$y_{cm}>0$ since all points of the rod which coincides with y-axis has y value $>$ 0.
B:
$x_{cm}=0$ due to symmetry.
$y_{cm}<0$ since cm of the two right rods will be below the x-axis and cm of the two left rods will also be below the x-axis.
C:
$y_{cm}<0$ since the upper semi circle has less mass than the upper semi circle.
$x_{cm}=0$ due to symmetry.
D:
cm of the right semi circle will be in the fourth quadrant.
cm of the left semi circle will be in the third quadrant.
$x_{cm}=0$ due to symmetry.
$y_{cm}<0$