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A balloon with mass m is decending down ...

A balloon with mass m is decending down with an acceleration a (where a `lt` g ) . How much mass should be removed from it so that it strts moving up with an acceleration a?

A

`(2ma)/(g + a)`

B

`(2ma)/(g - a)`

C

`(ma)/(g + a)`

D

`(ma)/(g - a)`

Text Solution

Verified by Experts

Let upthrust of air be `F_(a)`, then for downward motion
`mg - F_(a) = ma " " or, F_(a) = m(g - a)`
For upward motion, `F_(a) - (m - Delta m)g = (m - Delta m)a`
or, `Delta m(g + a) = ma + mg - F_(a) = 2 ma`
`therefore" " Delta = (2ma)/(g + a)`
The option A is correct.
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