A cube (density 0.5 gm/cc) of side 10 cm is floating in water kept in a cylindrical beaker of base area 1500 cm 2 . When an unknown mass is kept on wooden block the level of water rises in the beaker

Question

A cube (density 0.5 gm/cc) of side 10 cm is floating in water kept in a cylindrical beaker of base area 1500 cm 2 . When an unknown mass is kept on wooden block the level of water rises in the beaker by 2 mm . If the unknown mass is 75 α (in gm) then the value of α .

TestHub · Accepted Answer

Let the cube dips further by y cm and water level rises by 2 mm.

Initial situation

Final situation

Equate extra displaced volume:
$100 y = 1400 (0.2)$
$y = 2.8 cm$
Extra buoyant force equals the load:
$m g = ρ_{w} g (2.8 + 0.2) (100)$
$m = 300 g$
$300 = 75 α$
$α = 4$

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