A cylindrical wooden float whose base area is 4 m² and height 1 m floats on the water surface in vertical position. Density of wood is 500 kg/m³ and that of water 1000 kg/m³. What minimum work (in kJ) must be performed to take the float out of the water?
Physics · Mixed Chapter
JEE Mains

Question

A cylindrical wooden float whose base area is 4 m² and height 1 m floats on the water surface in vertical position. Density of wood is 500 kg/m³ and that of water 1000 kg/m³. What minimum work (in kJ) must be performed to take the float out of the water?

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1: The float is initially half submerged because ρ_wood/ρ_water=1/2; immersed depth is 0.5 m. Step 2: While it is pulled upward through distance x (0≤x≤0.5 m), the upward buoyant force decreases by ρ_water g A x. The required pulling force consequently rises linearly from 0 to ρ_water g A(0.5). Step 3: Work is the triangle area under F versus x: W=½ρ_water g A (0.5)². Step 4: W=½×1000×10×4×0.25=5000 J=5 kJ.