Question

A cuboid is filled with liquid of density ${\rho }_2$ upto height h and with liquid of density ${\rho }_1$ also upto height h as shown

$\begin{array}{cc}\text{Column I}& \text{Column II}\\ \text{(A) Force on face ABCD due to liquid of density}{\rho }_1& \text{(p) zero}\\ \text{(B) Force on face ABCD due to liquid of density}{\rho }_2& \left(q\right)\frac{{\rho }_{1}g{h}^{2}l}{2}\\ \text{(C) Force on face CDEF due to liquid of density}{\rho }_1& \left(r\right){\rho }_{1}g{h}^{2}l\\ \text{(D) Force on face CDEF due to liquid of density}{\rho }_2& \left(s\right)[{\rho }_{1}gh+\frac{{\rho }_{2}gh}{2}]hl\\ & \left(t\right)10{\rho }_{1}g{h}^2{l}^2\end{array}$

• A. A-q, B-r, C-p, D-s
• B. A-q, B-p, C-r, D-s
• C. A-p, B-q, C-r, D-s
• D. A-q, B-p, C-s, D-r

Answer 1

The correct option is B A-q, B-p, C-r, D-s

A - q ; B - p ; C - r; D - s
(A) On ABCD avg pressure $=\left[\frac{0+{\rho }_{1}gh}{2}\right]$
So $F=\left[\frac{{\rho }_{1}gh}{2}\right]\left[lh\right]=\frac{{\rho }_{1}g{h}^{2}l}{2}$
(B) No contact of liquid of density ${\rho }_2$ and not any pressure on ABCD due to liquid of density ${\rho }_2$
(C) On CDEF due to liquid of density ${\rho }_1$, at every point pressure is ${\rho }_{1}gh$ so average is also ${\rho }_{1}gh$ so $F=\left({\rho }_{1}gh\right)\left(hl\right)={\rho }_{1}g{h}^{2}l$
(D) On CDEF due to liquid of density ${\rho }_1$ is constant but due to liquid of density ${\rho }_2$ is variable, so pressure is
$[{\rho }_{1}gh+\left\{\frac{0+{\rho }_{2}gh}{2}\right\}]\left[hl\right]$

Why this question? Caution: Any liquid in a container, if it lies above a surface, then it will exert pressure on that surface whether it is in contact with the surface or not.