A balloon is descending with uniform acceleration a (a<g) . Weight of the balloon with basket and its content is W. What wight w of the ballast should be released so that the balloon will begin to rise with the same uniform acceleration a? Neglect air resistance.

Dear Student,

Please find below the solution to the asked query:

Given that the balloon is descending with acceleration a which is less than that of the acceleration due to gravity. This is due to the air resistance force F_r. So, the equation of motion is,


$Mg-F_r=Ma\Rightarrow F_r=M\left(g-a\right)$

Now, if we remove mass m from the basket, so that the balloon accelerates up with the same acceleration a. So,

$$\begin{gathered} F_r-\left(M-m\right)g=\left(M-m\right)a \\ \Rightarrow M\left(g-a\right)-\left(M-m\right)g=\left(M-m\right)a \\ \Rightarrow Mg-Ma-Mg+mg=Ma-ma\Rightarrow m\left(g+a\right)=2Ma \\ \Rightarrow m=\frac{2Ma}{g+a} \end{gathered}$$
 

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