Two cylindrical vessels of equal cross-sectional area 2 m² contain water up to heights 10 m and 6 m respectively. They are connected at the bottom. Take water density 1000 kg/m³ and g = 10 m/s². The work done by gravity is:
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Question

Two cylindrical vessels of equal cross-sectional area 2 m² contain water up to heights 10 m and 6 m respectively. They are connected at the bottom. Take water density 1000 kg/m³ and g = 10 m/s². The work done by gravity is:

Options

G1 Physics · Accepted Answer

After connection, the final water level in both equal-area vessels is the average height: h f h_f h f ​ = (10+6)/2 = 8 m. Only the excess water corresponding to a 2 m height difference effectively falls from the higher vessel to the lower vessel. A compact expression for the decrease in gravitational potential energy is W = (ρgA/4)(h₁-h₂)². Substitute, ρ = 1000 kg/m³, g = 10 m/s², A = 2 m², h₁-h₂ = 4 m. W = (1000×10×2/4)(4²) = 5000×16 = 8×10⁴ J. Correct option: B.