Copper and silver solid balls of the same volume are suspended at the ends of the lever 50 cm long.

Copper and silver solid balls of the same volume are suspended at the ends of the lever 50 cm long. at what distance from the middle of the lever should the fulcrum be placed so that the lever is in balance. Density of copper = 8900 kg / m3, density of silver = 10500 kg / m3.

F1 / F2 = l2 / l1, where l1 + l2 = 50 cm = 0.5 m.
F1 = Fт = m1 * g, where m1 is the mass of copper. ball (m1 = ρm * V1, where ρm = 8900 kg / m ^ 3, V1 is the volume of the copper ball).
F2 = Fт = m2 * g, where m2 is the mass of silver. ball (m2 = ρс * V2, where ρс = 10500 kg / m ^ 3, V2 is the volume of the silver ball).
From the condition of the problem: V1 = V2.
F1 / F2 = ρm * V1 * g / (ρс * V2 * g) = ρm / ρс = 8900/10500 = 0.85.
l2 / l1 = 0.85; l2 = 0.85 * l1.
l1 = 0.5-l2;
l2 = 0.85 * (0.5-l2) = 0.425-0.85 * l2.
1.85l2 = 0.425; l2 = 0.425 / 1.85 = 0.23 m.
l1 = 0.5-l2 = 0.5-0.23 = 0.27 m.
Answer: The fulcrum must be shifted 0.02 m towards the silver ball.