Answer
The center of mass of the leg is located at the point $(30~cm, 11.5~cm)$
Work Step by Step
We can find the coordinates of the center of mass of the 20-kg cylinder:
$x = \frac{35~cm}{2} = 17.5~cm$
$y = 0$
We can find the coordinates of the center of mass of the 10-kg cylinder:
$x = (35~cm)+(40~cm)~sin~30.0^{\circ} = 55~cm$
$y = (40~cm)~cos~30.0^{\circ} = 34.64~cm$
We can find the x-coordinate of the center of mass:
$x_{com} = \frac{(20~kg)(17.5~cm)+(10~kg)(55~cm)}{20~kg+10~kg}$
$x_{com} = 30~cm$
We can find the y-coordinate of the center of mass:
$y_{com} = \frac{(20~kg)(0)+(10~kg)(34.64~cm)}{20~kg+10~kg}$
$y_{com} = 11.5~cm$
The center of mass of the leg is located at the point $(30~cm, 11.5~cm)$.
