(i) When cubical block submerged into water –
By principle of floatation –
Vpg = V′ ρwg
\(\begin{bmatrix} V = Volumn\, of\, water\, displaced\ by'\, block \\ V'= column\, of\, block\, insider\, water\\ = area\, of \,base\, of\, block \times height \end{bmatrix}\)
V′ = L2x
V= Volume of block L3, ρB = Density of block
∴ L3ρB = L2xρw
⇒ \(\frac{ρ_B}{ρ_\text{w}}\) = \(\frac{x}{L}\) or x = \(\frac{ρ_B}{ρ_\text{w}}\) …(i)
(ii) When immersed block is in lift [moving in upward direction]
Then, net acceleration = g + a
Weight of block = m(g + a) = VρB(g + a) = L3ρB(g + a)
Let x1 be the part of block submerged into water in moving lift.
Weight of block = Buoyant force
L3ρB(g + a) = x1L2ρw(g + a) or \(\frac{ρ_B}{ρ_\text{w}}\) = \(\frac{x_1}{L}\)
Or x1 = L.\(\frac{ρ_B}{ρ_\text{w}}\) .........(ii)
From (i) & (ii), we conclude that it is independent of acceleration of lift.