Question

A cube of side 4 cm made of wood is floating in water of density 1gcc^-1. when a small steel ball is embedded in the cube it just immerses in water. If density of wood is 0.76gcc^-1, then mass of the ball is

Answer 1

Mass of the embedded ball = 15.36 g

Explanation:

The cube is floating.

Density = mass / volume

Density of wood = mass of cube / volume of cube

0.76 g / cm³ = mass / 64

Mass of cube = 64 * 0.76 = 48.64 g

Now, when the ball is embedded, it immerses in water.

The volume of water displaced is equal to the volume of the cube + ball.

Volume of cube + ball = 64 cm³

Density of water = 1  g / cm³

Mass of cube + ball = density of water * Volume of cube + ball

 Mass of cube + ball = 1 * 64

 Mass of cube + ball = 64 g

Therefore mass of ball = 64 - mass of cube  

  = 64 - 48.64

  = 15.36 g