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If I were to inflate a balloon with Helium inside it and were to leave the balloon under the water,will the balloon fly high in the sky cutting its way through water.If it does or doesn't somebody please explain.

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Let us assume you are capable of inflating a helium ballon under water, for example by using a helium bottle with sufficient pressure and a sufficiently robust balloon.

The inflated balloon will experience buoyancy, an upward force exerted on the ballon. The magnitude of this force is equivalent to the water weight of the volume that the balloon occupies. If the balloon's weight is lighter than the corresponding water weight, it will rise. And since helium has got a smaller density than water, this will happen (we can neglect the balloon weight for simplicity).

When the balloon reaches the surface, the surface tension will not be able to hold it under water so the balloon will break the surface. At this point, the same question arises: Is the balloon's weight smaller than the weight of the air that the balloon displaces. Since helium is less dense than air (roughly by a factor of 7) - yes, the balloon will rise into the sky. It will do so until it reaches a point where the atmosphere changes and the surrounding gases are less dense than helium.

In reality, other factors play a role: For example, the balloon would lose air due to the non-perfect seal and fall down earlier. But in an idealized situation, the above holds true.

For easy further reading: Archmiedes' principle, Buoyancy

Small edit: If you inflate the balloon at the beach and dive down with it, it will be compressed due to the pressure of the water. Nevertheless, it will still rise the way and for the same reasons I described above.

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    $\begingroup$ The weight of the balloon material itself should not be discounted. The final height will be lower than stated. $\endgroup$ – my2cts Jun 6 '18 at 8:14
  • $\begingroup$ As stated, I neglected it due to the anyway highly idealized situation. But you're right $\endgroup$ – lmr Jun 6 '18 at 8:25

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