We fully submerge an irregular 3 kglump of material in a certain fluid. The fluid that would have been in the space now occupied by the lump has a mass of 2 kg. (a) When we release the lump, does it move upward, move downward, or remain in place? (b) If we next fully submerge the lump in a less dense fluid and again release it, what does it do?

1. Mass of submerged lump, m= 3kg
2. Mass of fluid,$m_f=2kg$

Using the concept of buoyant force, we can calculate the buoyant force on the fluid by the mass of the object. To float the object in fluid, buoyant force must be greater than or equal to the weight of the object.

Formula:

The buoyant force acting on the fluid due to the weight of the object, $F_B=\rho Vg$ (i)

The weight of the object, $F_g=mg$ (ii)

a)

We know that to float an object in a fluid, the buoyant force must be greater than or equal to the weight of the object. Thus, using equations (i) and (ii), we get that

$F_B\ge F_g\left(W\right)$

As the mass of the submerged lump is greater than the mass of fluid, when the lump is released, it moves downwards.

b)

Due to less dense fluid, buoyant force will be less. Thus, we get the force as:

$F_B\ge F_g\left(W\right)$

Hence, the lump moves downwards due to greater weight than buoyant force.