A balloon carrying some sand of mass M is moving down with a constant acceleration $\mathrm{a}_0$. The mass…

A balloon carrying some sand of mass M is moving down with a constant acceleration $\mathrm{a}_0$. The mass ' $m$ ' of sand to be removed so that the balloon moves up with double the acceleration $\mathrm{a}_0$ is
  1. $m=\frac{2 M a_0}{a_0+g}$
  2. $m=\frac{2 M a_0}{a_0-g}$
  3. $m=\frac{3 M a_0}{g+2 a_0}$
  4. $m=\frac{3 M a_0}{g-2 a_0}$

Solution


From the figure, $\mathrm{Mg}-\mathrm{R}=\mathrm{Ma}_0$ ....(i) $R-(M-m) g=(M-m) a_0$ ....(ii) Adding eq(i) and (ii), we get $\begin{aligned} & \mathrm{Mg}-\mathrm{Mg}+\mathrm{mg}=(2 \mathrm{~m}-\mathrm{m}) \mathrm{a}_0 \\ & \Rightarrow \mathrm{~m}\left(\mathrm{~g}+\mathrm{a}_0\right)=2 \mathrm{Ma}_0 \\ & \therefore \mathrm{~m}=\frac{2 \mathrm{ma}_0}{\mathrm{~g}+\mathrm{a}_0} \end{aligned}$

Asked in: AP EAMCET 2024 (23 May Shift 1)

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