The maximum value of x is 0.39 m.
Given information:
Mass of each plank (m1) = 3.5 kg
Mass of the object (m2) = 2 kg
Density of the object (d) = 2 g/cm³
Length of each plank (L) = 1 m
The volume of the object:
V = m2 / d = 2 kg / 2 g/cm³ = 1000 cm³
Convert volume to length (assuming object is rectangular):
l = V / (L * L) = 1000 cm³ / (100 cm * 100 cm) = 0.1 m
The total mass on the left side:
Mleft = m1 + m2 = 3.5 kg + 2 kg = 5.5 kg
The torque due to the left side (counterclockwise):
τleft = Mleft * g * x
Calculate the torque due to the right side (clockwise):
τright = m1 * g * (L - x)
Set the torques equal at the point of balance (maximum value of x):
τleft = τright
Mleft * g * x = m1 * g * (L - x)
5.5 kg * g * x = 3.5 kg * g * (1 m - x)
5.5x = 3.5 - 3.5x
9x = 3.5
x = 3.5 / 9
x = 0.39 m