Question

A uniform solid cube is floating in a liquid as shown in the figure, with length $x$ inside the liquid. Some changes in parameters are mentioned in Column I. Assuming no other changes, match the following.

$\begin{array}{cc}\text{(A) If density of the liquid decreases,}x\text{will}& \text{(P) Increase}\\ \text{(B) If height of the cube is increased keeping base area and density same,}x\text{will}& \text{(Q) Decrease}\\ \text{(C) If the whole system is accelerated upward, then}x\text{will}& \text{(R) Remain same}\\ \text{(D) If the cube is replaced by another cube of same size but lesser density,}x\text{will}& \text{(S) either increase or decrease}\end{array}$

Which of the following option has the correct combination considering column-I and column-II.

• A.
  $D\to Q$
• B.
  $C\to P$
• C.
  $B\to R$
• D.
  $A\to R$

Answer 1

The correct option is A

$D\to Q$
As cube is floating-
$F_B=W_s{\rho }_{f}Axg={\rho }_{s}Algx=\frac{{\rho }_s}{{\rho }_f}\times l$

If density of liquid decreases and weight of cube is same
Buoyant force = Weight of cube
Cube will get more submerged.

$x=\frac{{\rho }_s}{{\rho }_f}\times l$
is independent of effective gravity


The fraction submerged is independent of total height.