Question

The pressures in a liquid at two points in the same horizontal plane are equal. Consider an elevator accelerating upward and a car accelerating on a horizontal road. The above statement is correct in

• A. the car only
• B. the elevator only
• C. both of them
• D. neither of them

Answer 1

The correct option is B

the elevator only

Consider a liquid placed in a beaker which is accelerated horizontally with an acceleration$a_0$ (say)

Let A& B be two points in a liquid at a separation L in the same horizontal line along the acceleration $a_0$

Consider a small vertical area $\Delta$ s around A& an equal area around B to construct a cylindrical surface.
The forces along the line AB are

(1) $P_{A\Delta s}$ towards right due to the liquid on the left

(2) $P_{B\Delta s}$ towards left due to the liquid on the right
Under the action of these forces, the liquid contained in the cylinder is accelerating towards right,
From Newton's 2nd law,

$P_{A\Delta s}-p_{B\Delta s}=m{a}_0$
$(P_A-P_B)\Delta s=\Delta spl{a}_0$

Where ρ = density of the liquid contained

$P_A-P_B=pl{a}_0$

$\Rightarrow$ it implies clearly that P_A> P_B and pressure in this case is not equal at same horizontal line.

You can also see it as the water column above A has increased due to the accelerated motion which justifies $P_A>P_B$ intuitively