a long non uniform board of length 8 m and mass m = 12 kg is suspended by two ropes if the tensions in the ropes are mg/3 (on left) and 2mg/3 (on right) what is the location of the board's center of mass

Question

thank you!

Answer 1

cg at x from left
then cg is at (8-x) from right

take moments about cg

(mg/3) (x) = (2 mg/3 )(8-x)

x = 16 - 2x
3 x = 16
x = 16/3