Question

A wooden cube supports mass 0.2 kg. If the mass is removed , then it's side rises by 2 cm . Find the side of cube​

Answer 1

$<b> <u> Heya! </b> </u>$

________________________________________________________

Ques. → A wooden cube floating in water supports a mass of 0.2 kg on its top. When the mass is removed , the cube rises by 2 cm. Find the side of the cube .

Solution → We know that ,

$<u>Decrease in weight = decrease in upthrust</u>$

•°• mg = (V) ( pw) ( g )

{ g gets cancelled on both sides }

=> m = V × Pw

= > 0.2 = ( 2 × 10^-2 )a × 10³

↑ here 'a' is the area of base of cube.

Thus , from the equation we get

A = 10^-2 m² = 100 cm²

So side of cube =>

L = √A

=> √100

$<b> <u>•°• Side of cube is 10cm!! </b> </u>$

____________________________________________________________________

Answer 2

$Hello userr,\\Let the edge of cube be ℓ. When mass is on the cube of wood\\200 g + ℓ3 d wood g = ℓ3 dwater g\\⇒ ℓ3 dwood = ℓ3 dwater – 200 … (i)\\When the mass is removed\\ℓ3 dwood = (ℓ - 2 ) ℓ2 dwater … (ii)\\From (i) and (ii)\\ℓ3 dwater - 200 = (ℓ- 2) ℓ2 dwater\\But dwater = 1\\∴ ℓ3 - 200 = ℓ2 (ℓ - 2)\\⇒ ℓ = 10 cm$