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A cube of wood supporting 200 gm mass just floats in water. When the mass is removed. The cube ruses by 2 cm. What is the size of the cube?

A cube of wood supporting 200 gm mass just floats in water. When the mass is removed. The cube ruses by   
2 cm. What is the  size of the cube?

Grade:upto college level

1 Answers

Navjyot Kalra
askIITians Faculty 654 Points
6 years ago
Let the edge of cube be ℓ. When mass is on the cube of wood
200 g + ℓ3 d wood g = ℓ3 dwater g
⇒ ℓ3 dwood = ℓ3 dwater – 200 … (i)
When the mass is removed
ℓ3 dwood = (ℓ - 2 ) ℓ2 dwater … (ii)
From (i) and (ii)
ℓ3 dwater - 200 = (ℓ- 2) ℓ2 dwater
But dwater = 1
∴ ℓ3 - 200 = ℓ2 (ℓ - 2)
⇒ ℓ = 10 cm

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