Q. An aquarium tank is in the shape of a cube with one side a 4m tall glass wall. When the tank is half filled and the water is 2 m deep, the water exerts a force $F$ on the wall. What force does the water exerts on the wall when the tank is full and the water is 4 m drop?
A) 1/2 $F$
B) $F$
C) $2\ F$
D) $4\ F$
Explanation
(d) Let $b$ be width of the glass wall. When the tank is half filled then the average force on the glass wall is
$F =$ average pressure $\times$area
$= \left\lbrack \left( \frac{4}{2} \right)\rho_{w}g \right\rbrack \times \left\lbrack \frac{4}{2} \times b \right\rbrack$
When tank is filled up to height 4 m, then
$F^{'} = \left( 4\ \rho_{w}g \right)(4 \times b)$
$\frac{F^{'}}{F} = \frac{4 \times 4}{2 \times 2} = 4$ or $F^{'} = 4F$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.