A balloon of mass ' M ' descends with an acceleration ' a ' , (

Question

A balloon of mass ' M ' descends with an acceleration ' a ' , (< g). What mass need to be removed from the balloon so that it starts ascending with acceleration ' a '? (A) (2 M/(a+ g)) (B) (2 M a/(a +g)) (C) (2 M a/(a -g)) (D) (2 M a/(g -a))

Tardigrade Admin · Accepted Answer

The given situation is shown in the figure

In above figures,

M

is the mass of balloon and

M^{'}

is the mass remove from the balloon.
According to Newton's law of motion in first case,

M g - F = M a \Rightarrow F = M g - M a \dots

(i)
According to Newton's second law of motion, for second case,

F - (M - M^{'}) g = (M - M^{'}) a

\Rightarrow F - M g + M^{'} g = M a - M^{'} a

\Rightarrow M g - M a - M g + M^{'} g = M a - M^{'} a

[ from Eq. (i)]

\Rightarrow M^{'} g + M^{'} a = M a + M a

\Rightarrow M^{'} (g + a) = 2 M a

\Rightarrow M^{'} = \frac{2 M a}{g + a}

Q. A balloon of mass ' $M$ ' descends with an acceleration ' $a$ ' , $(< g)$ . What mass need to be removed from the balloon so that it starts ascending with acceleration ' $a$ '?

$\frac{2 M}{( a + g )}$

$\frac{2 M a}{( a + g )}$

$\frac{2 M a}{( a - g )}$

$\frac{2 M a}{( g - a )}$

Q. A balloon of mass ' M ' descends with an acceleration ' a ' , (<g). What mass need to be removed from the balloon so that it starts ascending with acceleration ' a '?

(a+g)2M​

(a+g)2Ma​

(a−g)2Ma​

(g−a)2Ma​

Q. A balloon of mass ' $M$ ' descends with an acceleration ' $a$ ' , $(< g)$ . What mass need to be removed from the balloon so that it starts ascending with acceleration ' $a$ '?

$\frac{2 M}{( a + g )}$

$\frac{2 M a}{( a + g )}$

$\frac{2 M a}{( a - g )}$

$\frac{2 M a}{( g - a )}$