You just have to tell whther I'm right or Wrong and Why..No need to do any calculations :

To all folks in TargetIIT , I'm weak in mechanics especially Fluid Mechanics and I don't know even the basic concepts [2] .

In the quest for more concepts..I'm posting an analysis of a fluid statics concept regarding Archimedes Principle , JUST TELL ME WHETHER I'M WRONG OR RIGHT AND IF I'M WRONG THEN WHY..

Q: A wooden block[M] with a coin[m] placed on its top , floats in water as as shown in the figure [given below] .The distance L,x and h are shown these.After sometime the coin falls into the water.Then :

[A] x decreases and h increases

[B] x increases and h decreases

[C] both increase

[D] both decrease

Answer given : D

My Mathematical solution :

I assumed the following :

A : Base area of container
d : Density of block
d_coin : Density of coin [I think it is always greater than d ,rt ? ]
x₁ and x₂ :Different values of x before and after coin falls
h₁ and h₂ :Different values of h before and after coin falls.

Initially [ before coin falls ] :

Height of water displaced = h₁ = x₁L(M+m)d.A------------------------(1)

Finally [after coin falls ] :

Height of water displaced = h₂ = x₂LMd.A+md_coin.A---------------(2)

-> Now as coin falls from the block , it is obvious that x₂ < x₁ [so x decreases]

Now h₁-h₂ = M(x₁-x₂)L.d.A +mA(x₁L.d - 1d_coin)

Doubt 1 : Isn't the answer [D] , only when x₁=L ( I mean , h₂ <h₁ only when it is initially x₁=L right ? ) ?

Doubt 2 : From (1) and (2) ,we can see that the term d is in the denominator so: I conclude that , as the density of the floating material ( d ) increases , the level of the liquid in which it floats ( h )[here it is water] decreases , AM I RIGHT / WRONG..if I 'm wrong , then please give the reason ...