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

Answer :

Let ρ represent the density of a block and let height of the block be L

Then, we can write the expression for the mass of the block as follows:

m = Vρ = L³ρ

Then, the weight of the block is

mg = L³ρg

Let x represent the height of the cube submerged.

Case II

When the vessel is placed on an elevator that accelerates upwards at a constant rate, the acceleration is equal to (g + a).

The weight of the block is given in the follwoing manner

m(g + a) = L³ ρ(g + a)

Therefore, the expression for effective weight becomes

m (g + a)

Let x_{1 be the} new fraction of block submerged in water. Then, we have –

${{x}_{1}}=\frac{m}{{{L}^{3}}{{\rho }_{w}}}=\frac{{{L}^{3}}\rho }{{{L}^{3}}{{\rho }_{w}}}=\frac{\rho }{{{\rho }_{w}}}=x$