Question

An air-filled balloon floats in water with half of its volume submerged. To what depth inside water should it be taken so that ir remains in equilibrium there? Take atmospheric pressure to be equal to $10m$ of water-height.

• A. $5m$
• B. $10m$
• C. $15m$
• D. $20m$

Answer 1

The correct option is B $10m$

Let it taken to depth $\left(h\right)$

as temp remain constant

So, $P_{0}V=(P_0+Pgh)V^{\prime }$

at depth $\left(h\right)$ net force is $O$

So, $mg=B$

$mg=V^{\prime }Pg$

$mg=Pg\left(\frac{P_{0}V}{P_0+Pgh}\right)$

$\frac{m}{v}=P\left(\frac{P_0}{P_0+Pgh}\right)$

$\frac{\text{Density of body}}{P}=\frac{{10}^5}{{10}^5+{10}^{4}h}$

$P_0=10\times {10}^3\times 10$

$={10}^5$

$\frac{{10}^5}{2}+\frac{{10}^4}{2}h={10}^5$

$\Rightarrow \frac{{10}^4}{2}h=\frac{{10}^5}{2}$

$\Rightarrow h=10m$