A balloon of total mass ‘M’ and a fixed size starts coming down w… - Vidyadip

MCQ

A balloon of total mass $‘M’$ and a fixed size starts coming down with an acceleration $f(f < g)$ . The fraction of the total mass of the balloon which must be dropped from it so that it starts going up with an acceleration of $‘f’$ (assuming negligible air resistance) is

A
$\frac{f}{{g + f}}$
✓
$\frac{{2f}}{{\left( {g + f} \right)}}$
C
$\frac{{g + f}}{f}$
D
$\frac{{2f}}{{g + 2f}}$

✓

Answer

Correct option: B.

$\frac{{2f}}{{\left( {g + f} \right)}}$

b
$\mathrm{Mg}-\mathrm{B}=\mathrm{Mf}$

$\mathrm{B}-(\mathrm{M}-\mathrm{CM}) \mathrm{g}=(\mathrm{M}-\mathrm{CM}) \mathrm{f}$

$\mathrm{CMg}=(2 \mathrm{M}-\mathrm{CM}) \mathrm{f}$

$\mathrm{Cg}+\mathrm{Cf}=2 \mathrm{f}$

$\mathrm{C}=\frac{2 \mathrm{f}}{\mathrm{g}+\mathrm{f}}$

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