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  4. A hot air ballon of mass M is descending vertically downward with acceleration a. How much mass must be removed to give ballon an upward acceleration of a?

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Q. A hot air ballon of mass $M$ is descending vertically downward with acceleration $a$. How much mass must be removed to give ballon an upward acceleration of $a$?

UP CPMTUP CPMT 2011

Solution:

Let $F$ be constant upthrust force and $m$ is the removed mass.
Free body diagram for case $(1)$.
image
$(Mg - F) = Ma \quad ...(i)$
Free body digram for case $(2)$
image
$F - (M -m)g = (M -m )a \quad ...(ii)$
Adding $(i)$ and $(ii)$, we get
$mg = 2 Ma - ma$
$m(g + a) = 2 Ma$
$m = \frac{2Ma}{(g+a)}$