Question

A block of wood floats in a bucket of water placed in a lift. Will the block sink more or less if the lift starts accelerating up?

Answer 1

Let the density of wood be $b$ and water be $w$.

we can assume initially volume $v$ is immersed in liquid of total volume V.

Balancing the buoyancy force,

So $vwg=bVg$ .....(1)

So we get $\frac{v}{V}=\frac{b}{w}$ ...(2)

Now when lift starts moving up, lets assume that volume $v_1$ is immersed

$v_{1}w(g+a)=bV(g+a)$ ....(3)

From equation 1, we can write $v_{1}w=bV$

$\frac{v_1}{V}=\frac{b}{w}$ ...(4)

comparing 4 and 2 we can say $v_1=v$, so the block will float with same level of volume immersed in water,