Question

A balloon with mass 20 kg is moving downward with an
aeceleration 2.2 m/s2. What mass Am of its contents be
remoyed so that it starts moving up with same acceleration?
(g = 9.8 m/s2)
2.66 kg
7.33 kg
4.66 kg
5.33 kg​

Answer 1

Given:

A balloon with mass 20 kg is moving downward with an acceleration 2.2 m/s².

To find:

Mass removed so that it starts moving up with same acceleration?

Calculation:

Initially, in downward movement, we can say:

• $F_{B}$ is buoyant force.

$\rm \: Mg - F_{B} = Ma$

$\rm \implies\: 20(9.8) - F_{B} = 20(2.2)$

$\rm \implies\: F_{B} = 20(9.8- 2.2)$

$\rm \implies\: F_{B} = 20(7.6)$

$\rm \implies\: F_{B} = 152\: N$

Now, in reduced mass , body moves upwards:

$\rm \: F_{B} - mg = ma$

$\rm \implies\: 152 = m(g + a)$

$\rm \implies\: 152 = m(9.8 + 2.2)$

$\rm \implies\: 152 = 12m$

$\rm \implies\: m = 12.67 \: kg$

So, mass removed is :

∆m = M - m = 20 - 12.67 = 7.33 kg.