Answer:
Let x be the overhang of the plank
(4 - x) = Y portion of plank less the overhang
Y / 2 M g = clockwise torque due to weight of plank
40 x = counterclockwise torque due to weight of woman
(4 - x) M g / 2 = 40 x
(4 - x) M g = 80 x (I)
4 M g = (80 + M g) x (II)
x = 4 M g / (80 + M g) = 4 / (80 / M g + 1)
x would be shorter with an increase in M
if x were 1 then
4 M g = 80 + M g using (II)
M = 80 / (3 g) = 2.72 kg
Check: use x = 1 in equaton (I)
3 M g = 80
M = 80 / (3 * 9.8) = 2.72 kg
