Question

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?

Short answer

1. Movement ofblockswhen we release the lump is downward.
2. Movement of blocks when we release the lump in less dense fluid is downward.

Step-by-step solution

The given data 

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

Understanding the concept of the buoyant force

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)

Calculation of the movement of the blocks if lump is released

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.

Calculation of the movement of the blocks when the fluid is less dense

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.