Question

You are given a solid ball of mass 15 gram and a hollow iron ball of volume 20 cm cube and mass 15 gram both are placed on the surface of water which ball will sing give reason density of iron is equal to 7.8 gram per centimetre cube

Answer 1

We know that the upthrust of an object placed in water is given by

U = (V x ρ - m) x g

where V = volume of water displaced = volume of object

ρ = density of water = 1 g/cm³

m = mass of ball

g = acceleration due to gravity = 10 m/s²

volume of 1st ball = mass/density = 15/7.8 = 1.92 cm³

Putting all the values in the above eqn,

For 1st ball

U₁ = (1.92 x 1 - 15) x 10 = -130.8

For 2nd ball,

U₂ = (20 x 1 - 15) x 10 = 50

Since the upthrust for 1st ball is negative hence 1st ball will sink

The reason behind this is for 1st ball the upward buoyant force is less than its downward weight so the first ball will sink.