A cubical block of density `rho` 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 ?

Explanation

Consider the diagram.
Let the density of water be `rho_(w)` and a cubical block of ice of side L be floating in water with `x` of its height (L) submerged in water.
Volume of the block `(V)=L^(3)`
Mass of the block `(m)=Vrho=L^(3)rho`
Weight of the block `=mg=L^(3)rhog`

1st case
Volume of the water displaced by the submerged part of the block `=xL^(2)`
`therefore` Weight of the water displaced by the block
In floating condition, `xL^(2)rho_(w)g`
Weight of the block=Weight of the water displaced by the block
`L^(3)rhog=xL^(2)rho_(w)g`
or `(x)/(L)=(rho)/(rho_(w))=x`
2nd case
When elevator is acceleration upward with an acceleration a , then effective acceleration
`=(g+a) " "`( `because` Pseudo force is downward)
Then, weigth of the block
`m=(g+a)`
`" "=L^(3)rho(g+a)`
Let `x_(1)` fraction be submerged in water when elevator is accelerating upwards.
Now, in the floating condition, weight of the block =weight of the displaced water
`L^(3)rho(g+a)=(x_(1)L^(2))rho_(w)(g+a)`
or `(x_(1))/(L)=(rho)/(rho_(w))=x`
From 1st and 2nd case,
We see that , the fraction of the block submerged in water is independent of the acceleration of the elevator.
Note We should not confuse with the concept of pseudo force, i.e., pseduo force is downward, hence fraction will change due to increased force.