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Laws of Motion question

2014 · Q142
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Laws of Motion question

2014 · Q142

NEETPhysicsLaws of MotionMCQ+4 / −1
A balloon with mass m is descending down with an acceleration a (where a < g). How much mass should be removed from it so that it starts moving up with an acceleration a ?
  1. A
    2mag+a{{2ma} \over {g + a}}g+a2ma​
  2. B
    2mag−a{{2ma} \over {g - a}}g−a2ma​
  3. C
    mag+a{{ma} \over {g + a}}g+ama​
  4. D
    mag−a{{ma} \over {g - a}}g−ama​
View written solutionFree

Correct answer: A

Let upthrust of air be Fa then

For downward motion of balloon

Fa = mg – ma

mg – Fa = ma

For upward motion
Fa−(m−Δm)g=(m−Δm)a{F_a} - \left( {m - \Delta m} \right)g = \left( {m - \Delta m} \right)aFa​−(m−Δm)g=(m−Δm)a

⇒\Rightarrow⇒ Δm=2mag+a\Delta m = {{2ma} \over {g + a}}Δm=g+a2ma​

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