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Laws of Motion

Section: Physics

Question : 5 of 20

Marks: +1, -0

m

a

a < g

Solution:

When the balloon is descending, the net force acting on it is given by

F_{\text{net}} = mg - B = ma

, where

B

is the Buoyant force.

Thus,

B = mg - ma

For the balloon to move upwards with the same acceleration

a

, a mass

\Delta m

must be removed. The new net force equation becomes

B - (m-\Delta m)g = (m-\Delta m)a

mg - ma - (m-\Delta m)g = (m-\Delta m)a \quad [\text{From Eq. (i)}]

\Rightarrow \quad \Delta m = \frac{2ma}{g+a}

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