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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

Verified by Experts

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
    `(2ma)/(g+a)`
    B
    `(2ma)/(g-a)`
    C
    `(ma)/(g-a)`
    D
    `(ma)/(g-a)`

  • A balloon of mass m is rising up with an acceleration a.

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

  • A balloon of mass M and a fixed size starts coming down with an acceleration f(fltg). The ballast mass m to be dropped from the ballon to have it go up with an acceleration f. Assuming negligible air resistance is find the value of m

    A
    `(M/(g+f))f`
    B
    `(Mf)/(2(g+f))`
    C
    `((2Mf)/(g+f))`
    D
    `(m(g+a))/(g)`