A) \[\frac{a}{a+g}M\]
B) \[\frac{g}{a+g}M\]
C) \[\frac{2a}{a+g}M\]
D) \[\frac{2g}{a+g}M\]
Correct Answer: C
Solution :
The forces acting on the balloon when the balloon is coming downwards with an acceleration \[a\] are (i) weight, \[mg\] acting downwards and (ii) force of upthrust, \[F\] acting upwards. Since the accelerated movement is in downward direction, the force Mg must be greater than\[F\]. So for the downwards accelerated movement of the block,\[Mg-F=Ma\] ... (i) Let \[m\] be the mass removed from the balloon, the weight of the balloon now becomes\[(M-m)g\]. Now for the upward accelerated movement with same acceleration, we have\[F-(M-m)g=(M-m)\] ... (ii) Solving equations, (0 and (ii) the correct option can be seen to be [c].
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