Question

• A 2 cm block floats with 1/3 of its volume above the water. Find the density of the block.
• Find the amount of mass required to submerge the block.

Answer 1

Let the volume of the block be Vcm3 = 8 and its density be dcm−3

So the weight of the block =Vdg dyne, where g is the acceleration due to gravity =980cms−2

The block floats in liquid of density 1 gcm−3 with 2/3rd of its volume submerged.So the upward buoyant force acting on the block is the weight of displaced liquid=2/3 V×1×g dyne.

Hence by condition of floatation

V×d×g=2/3×V×1×g

⇒d=0.667 gcm-3,

Let the amount of mass required be m.

mg= 1/3 V x 1 x g

m= 2.667 gm