Question

If $F$ force is applied on area $\frac{A}{2}$, the value of pressure is $P_1$. If we change the force to $2F$ and area to $2A$, then calculate the change in pressure.

Answer 1

We know that, pressure is a pure ratio of force and area.
$⟹Pressure=\frac{Force}{Area}$
Given:
For force $F$ and area $\frac{A}{2}$, the value of pressure is $P_1$.

$⟹P_1=\frac{F}{\frac{A}{2}}=\frac{2F}{A}$
Let the pressure be $P_2$ when the force is $2F$ and area is $2A$.

$P_2=\frac{2F}{2A}=\frac{F}{A}$

Now change in pressure,
$P_2-P_1=\frac{F}{A}-\frac{2F}{A}=-\frac{F}{A}$

(negative sign shows that there is decrease in pressure)
Hence, the change in pressure is $\frac{F}{A}$.