Question

A cubical container which is completely filled with an ideal fluid, moves in a gravity free space with a acceleration of $a=a_0(\hat{i}-\hat{j}+\hat{k})$ ; where $a_0$ is a positive constant. The points in the container where pressure is maximum and minimum are:

• A. $F$ and $H$
• B. $E$ and $F$
• C. $C$ and $B$
• D. $B$ and $H$

Answer 1

The correct option is D $B$ and $H$

Given acceleration $a=a_0(\hat{i}-\hat{j}+\hat{k})$

Direction of pseudo force is opposite to acceleration.
direction of pseudo force is along $-a=a_0(-\hat{i}+\hat{j}-\hat{k})$

In cube pressure is generated due to pseudo force.
Hence pressure is maximum in the direction of pseudo force and minimum in the direction of acceleration.

by the given acceleration minimum pressure will be on :
$DCGH$ due to pseudo force in -x direction
$EFGH$ due to pseudo force in +y direction
$ADHE$ due to pseudo force in -z direction
the only common vertex is H.
so minimum pressure will be at H.

by the given acceleration maximum pressure will be on :
$ABFE$ due to pseudo force in -x direction
$ABCD$ due to pseudo force in +y direction
$BCGF$ due to pseudo force in -z direction
the only common vertex is B.
so maximum pressure will be at B.