A wooden block is floating in a liquid, 50% of its volume is inside the liquid when the vessel is stationary. Percentage of volume immersed when the vessel moves upwards with an acceleration $a = g / 2$ is:

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$50 %$

$25 %$

$75 %$

$33.33 %$

answer is C.

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Detailed Solution

When the vessel is stationary:
Weight = upthrust
i.e., $V ρ_{w} g = V_{i} ρ_{L} g$
( density of wood and $ρ_{L} =$ density of liquid)
Or    $\frac{V_{i}}{V} = \frac{ρ_{w}}{ρ_{L}} ............. (i)$
When the vessel moves upwards:
Upthrust – weight = (mass) (acceleration)
Or $V'_{i} ρ_{L} (g + g / 2) - V_{ρ_{w}} g = \frac{V ρ_{w} g}{2}$
Or $\frac{V'_{i}}{V} = \frac{ρ_{w}}{ρ_{L}} .......... (i i)$
From Eqs. (i) and (ii), we see that
   $\frac{V_{i}}{V} = \frac{V'}{V}$
i.e., fraction (or percentage) or volume immersed in liquid remains unchanged.