A cubical block is floating in a liquid with half of its volume immersed in the liquid. When the whole system accelerates upwards with acceleration of `g//3`, the fraction of volume immersed in the liquid will be

Options

A. `1//2`
B. `3//8`
C. `2//3`
D. `3//4`

Answer

A

Explanation

Let x be the fraction of volume immersed in first case and y the fraction in second case.
Then in first case, W= Upthrust
or `Vrho_(b)g=(xV)rho_(l)g " or" x=(rho_(b))/(rho_(l))`
In second case,
Upthrust-weight = mass `xx` acceleration
or `(yV)rho_(l)(g+g//3)-(Vrho_(b))g=(Vrho_(b))((g)/(3)) " or" y=(rho_(b))/(rho_(l))`
From Eqs. (i) and (ii), we see that x=y or fraction of volume immersed does not change by the acceleration of vessel.