Question

Consider the equations
$P=\underset{∆s\to 0}{\lim }\frac{F}{∆S}\mathrm{and}{P}_1-P_2=\rho gz.$
In an elevator accelerating upward
(a) both the equations are valid
(b) the first is valid but not the second
(c) the second is valid but not the first
(d) both are invalid

Answer 1

(b) the first is valid but not the second

For a point inside the elevator, pressure can be defined as $P=\underset{∆s\to 0}{\lim }\frac{F}{∆S}$. It is independent of the acceleration of the elevator.

The modified form of the second equation, which will be valid in the given case, is given by
$P_1-P_2=\rho (g+a_0)z$
Here, acceleration a₀ (say) due to elevator accelerating upwards is also taken into account.$$