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# A balloon of mass 30 kg is falling down with an acceleration of $1.8m/s^{-2}$.Then some mass is removed from the balloon.As a result the balloon moves upwards with an acceleration of $2.2 ms^{-2}$. The mass removed from the balloon is

$(a)\;16 kg\quad (b)\;10 kg \quad (c)\;18 kg \quad (d)\;12 kg$

Let new mass be $m_1$
$mg-N=ma_1$
$30 \times 9.8-N=30 \times 1.8$
$N=30 \times (9.8-1.8)$
$\quad= 30 \times 8$
$N-m_1g=m_1a_2$
$30 \times 8 -m_1 \times 9.8 =m_1 2.2$
$m_1=\large\frac{30 \times 8}{(9.8+2.2)}$
$\qquad=\large\frac{30 \times 8}{12}$
$\qquad=20\;kg$
So the mass removed $=30-20=10\;kg$
Hence b is the correct answer.

edited Feb 10, 2014 by meena.p