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A cubical block of density ρ is floating on the surface of water. Out of its height L, fraction x is submerged in water. The vessel is in an elevator accelerating upward with acceleration a. what is the fraction immersed?

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(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

∴ L3ρ= L2w
⇒ \(\frac{ρ_B}{ρ_\text{w}}\) = \(\frac{x}{L}\) 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 x= L.\(\frac{ρ_B}{ρ_\text{w}}\)      .........(ii)

From (i) & (ii), we conclude that it is independent of acceleration of lift.

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