Question

a cube is floating in water, when 2g is placed on the cube ,the cube is completely immersed in the water. determine the volume of cube
help me!!!

Answer 1

Let the side of the cube be S, density of water be d, mass of cube be m, acceleration due to gravity be g.

When the weight is on the block,

Using Archimedes’ Principle ,

Weight of the block + Weight of the mass = Bouyant force (B1)

(Since B1 = volume of water displaced = S3×d×gS3×d×g )

=> m×g+0.2×g=S3×d×gm×g+0.2×g=S3×d×g

=> m=S3×d+0.2m=S3×d+0.2 …. 1

When the mass is removed,

Weight of the block = Bouyant force (B2)

(Since B2 = (S−0.02)S2×d×g(S−0.02)S2×d×g)

=> m×g=(S−0.02)S2×d×gm×g=(S−0.02)S2×d×g

=> m=(S−0.02)S2×dm=(S−0.02)S2×d … 2

From 1 and 2,

S3×d+0.2=(S−0.02)S2×dS3×d+0.2=(S−0.02)S2×d

=>0.2=0.02×S2×d0.2=0.02×S2×d

Taking d = 1000kg/m31000kg/m3

S2=0.01S2=0.01

=> S = 0.1 m = 10cm³

HOPE YOU ARE SATISFIED WITH MY ANS