Question

Two identical cylinders are connected by a pipe. In both cylinders we fill water partially and float two smaller cylinders as shown. The left cylinder has area S₁ & right one has area S₂. These cylinders are both massless. They are filled with equal volume of water (V). Now in left cylinder we float a block of mass m₁ and in right cylinder we float a block of mass m₂. Before floating, the level in floating cylinders differed by x₁ & level in lower cylinders differed by y₁. The same values after floating are x₂ & y₂ respectively.

• A. x₁ = V($₁ -$₂)
• B. y₁ = 0
• C. x₂ = (m₁-m₂)(S₁-S₂) / pS₁S₂
• D. y₂ = (m₁-m₂) / pS₂

Answer 1

Answer: (B)

y₁ = 0

Answer 2

Initially, the two outer cylinders are connected by a pipe and contain equal volumes of water. Due to the pipe connection, the water levels in the outer cylinders will equalize to maintain the same pressure at the level of the pipe. Therefore, the difference in water levels in the lower (outer) cylinders before floating any masses, $y_1$, must be zero.