Question

The force $\left(F\right)$ that needs to be applied on water in the thicker arm so that the water may remain in equilibrum is

• A. $250\text{N}$
• B. $180\text{N}$
• C. $225\text{N}$
• D. $200\text{N}$

Answer 1

The correct option is C $225\text{N}$

For a static liquid (liquid at rest), Pascal's law suggests that pressure in the liquid at the same level must be equal.


Now, here water is in equilibrium, so equating the pressure in both arms,
$P_1=P_2...\left(i\right)$
Since atmospheric pressure $\left(P_0\right)$ is acting on both arms, it will cancel out from both sides.
Eq.$\left(i\right)$ can be written in terms of force acting on both arms as,
$\frac{F_1}{A_1}=\frac{F_2}{A_2}$
$\Rightarrow \frac{15\text{N}}{1{\text{cm}}^2}=\frac{F}{15{\text{cm}}^2}$

$\therefore F=225\text{N}$
Force of $225\text{N}$ needs to be applied on water in the thicker arm.