Q. 48

# A balloon filled

According to Archimedes principle when a body is partially or fully dipped into a fluid at rest, the fluid exerts an upward force of buoyancy equal to the weight of the displaced fluid.

The balloon similarly experiences a buoyant force which provides it an acceleration .

If

are the mass , density and volume of the balloon andis the density of

.

Then,

Now writing acceleration a, in its differential form,

Integrating both the sides, we obtain,

Now for the height by which it raises till time t, we use equation of motion

Putting the value of a and initial velocity to be zero,

now the kinetic energy of the balloon at time t,

K.E

Rearranging the terms, we get,

But are terms which represent potential energy of air and helium balloon respectively.

So, we can say the balloon raises by pushing the air downward, thus its potential energy increases as the air’s decreases.

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