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

Let density of water is `rho_(w)`. A block of height L float on it .x be the height of block submerged in water .
Volume of block `V=L^(3)`
Mass of block `m=Vrho=L^(3)rhog`
Weight of the block `=mg=L^(3)rhog`

First Case : Volume of part of cube submerged in water `=xL^(2)`
`therefore` Weight of water displaced by block `=xL^(2)rho_(w)g`
Weight of block =weight of water displaced by block .
`L^(3)rhog=xL^(2)rho_(w)g`
`therefore(x)/(L)=(rho)/(rho_(w))`
`thereforex=(rho)/(rho_(w))L`....(1)
Second Case : When vessel is placed in an elevator moving upward with acceleration a , then effective acceleration =g=(g+a)
More acceleration a is due to Pseudo force
`therefore` Weight of block =mg
`=m(g+a)`
Suppose , and elevator is moving upward .Let new fraction of block submerged in water is `x_(1)`
For floating of block ,
Weight of block =Weight of displaced water ,
`L^(3)rho(g+a)=x_(1)L^(2)rho_(w)(g+a)`
`therefore(x_(1))/(L)=(rho)/(rho_(w))`....(2)
`x_(1)=(rho)/(rho_(w))*L`
From equation (1)and (2) ,
`x=x_(1)`
Hence , the fraction of the block submerged is independent of acceleration.