Two wooden blocks `A` and `B` float in a liquid of density `rho_(L)` as shown. The distance `L` and `H` are shown. After some time, block `B` falls into the liquid, so that `L` decreases and `H` increases. If density of block `B` is `rho_(B)`, find the correct option.

Options

A. `rho_(L)=rho_(B)`
B. `rho_(L)gtrho_(B)`
C. `rho_(L)ltrho_(B)`
D. unpredicable

Answer

B

Explanation

As block `B` falls, `L` will decrease
Block `B` will displace volume of liquid `(V_(1))`
Equal to its own volume when it is in the liquid
`V_(1)=V_(B)=(M_(B))/(rho_(B))`……i
When block `B` is on block `A`, it will displace the volume of liquid `(V_(2))` whose weight is equal to the weight of the block `B`
`V_(2)rho_(L)g=M_(B)g=-(V_(1)rho_(B))g`
or `V_(2)rho_(L)=V_(1)rho_(B)`
Since `H` increase `V_(1)gtV_(2)`
So `rho_(L)gtrho_(B)`