What is the Maximum Weight of a Concrete Block Underwater?

[Delhi]

Hello, I would like to ask if my calculations are correct and which approach I should use if the answer is correct (I apologize if my calculations look ugly, just joined this forum).

Homework Statement

On land, the maximum weight of a concrete block you can carry is 25kg. How massive block could you carry underwater, if the density of concrete is 2200kg/m³?

p_water = 1000 kg/m³
p_concrete = 2200 kg/m³
m1 = 25 kg
m2 = ?

G = mg
g = 9,81 m/s²

Homework Equations

Archimedes' Principle

F_applied - G + F_buoyancy = 0
G - F_buoyancy

The Attempt at a Solution

Approach 1:

F_applied - G + F_buoyancy = 0 ->
m₁g - m₂g + m₂p_waterg / p_concrete = 0

And I come to this:

m₂ = -m₁ / ( (p_water/p_concrete) - 1 )

m₂ = 45,8333... kg


Approach 2:

On land I need (F= mg) 245,25 N to carry the concrete block

G - F_bouyancy = 245,25 N
m₂g - m₂g(p_water / p_concrete) = 245,25N
m₂g(1 - p_water / p_concrete) = 245,25 N
m₂ = 245,25N / g(1 - p_water / p_concrete)

m₂ = 45,8333... kg

 

[Quinzio]

I'd say it's correct.

In a more "elegant" form:

m' = m\frac{\rho_{conc}}{\rho_{conc}-\rho_{water}}

 

[Delhi]

I'd say it's correct.

In a more "elegant" form:

m' = m\frac{\rho_{conc}}{\rho_{conc}-\rho_{water}}

Yes that looks elegant. This might sound like a stupid question but from which formula do you get two \rho_{conc} ?