First slide

Second law

Question

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

Moderate

A

$\frac{2 m a}{g + a}$
B

$\frac{2 m a}{g - a}$
C

$\frac{m a}{g + a}$
D

$\frac{m a}{g - a}$

Solution

When the balloon is descending down with acceleration a,
$m g - B = m \times a . . . . . (i)$
where, B = Buoyant force.
Here, we should assume that while removing some mass, the volume of balloon and hence, buoyant force will not change.
Let the new mass of the balloon is m'.
So, mass removed = m - m'
When the balloon is moving up with acceleration a, then
$B - m^{'} g = m^{'} \times a . . . . . (ii)$
Adding Eqs. (i) and (ii), we get
$\Rightarrow m g - m^{'} g = m a + m^{'} a$
$\Rightarrow (m g - m a) = m^{'} (g + a)$
$\Rightarrow m (g - a) = m^{'} (g + a)$
$∴ m^{'} = \frac{m (g - a)}{(g + a)}$
So, mass removed,
$Δ m = m - m^{'} = m [1 - \frac{(g - a)}{(g + a)}] = m [\frac{(g + a) - (g - a)}{(g + a)}]$
$= m [\frac{g + a - g + a}{g + a}] = \frac{2 m a}{g + a}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App