Question

The collapsible balloon is inflated to a volume of $10L$, at a pressure of $1atm$. When the balloon is immersed to the bottom of a lake, its volume reduces to $1.25L$. Assuming atmospheric pressure to be equivalent to $10m$ column of water and no change in temperature. If the depth of the lake is $x\times {10}^{3}cm$, then the value of $x$ is:

Answer 1

According to ideal gas equation, at same temperature:
$P_1{V}_1=P_2{V}_2$

$10\times 10=1.25P,\Rightarrow P=80$
So, depth of water is $80-10=70m=7000cm=7\times {10}^{3}cm$.

So, $x$ is $7.$