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A balloon with mass m is descending down...

A balloon with mass `m` is descending down with an acceleration a `(where altg)` . How much mass should be removed from it so that it starts moving up with an acceleration a?

Text Solution

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Let the retarding force acting on the ballon in vertically upwards direction be `F`
When the ballon is descending down with acceleration its equation of motion can be written as
`Ma = M g - F or F= mg - Ma`
Let a mass m be removed from the balloon As it moves up with an acceleration a as shown in its equation of motion can be written as
`(M - m) a =F - (M - m) g`
using (i) `Ma - ma = Mg - Ma - M g + mg`
`2 M a = m (g + a)`
`m = ( 2Ma)/(g + a )`
.
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Knowledge Check

  • A balloon with mass m is descending down with an acceleration a where a

    A
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    B
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    The upthrust on the balloon is ma.
    C
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    D
    m/2 mass must be detached in order to double its acceleration.

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