Q101 / 180 · NEET 2014 · Physics

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 $a$ ?

Correct answer
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

Let the upward force be $F$ .

When balloon descending down, then $m g - F = m a$ …(i)

Let the mass removed be $m'$ .

When balloon ascending upward, then $F - (m - m^{'}) g = (m - m') a$
from (i)
$F - m g + m^{'} g = m a - m' a$
$m g - m a - m g + m^{'} g = m a - m' a$
$m^{'} (g + a) = 2 m a$
$m^{'} = \frac{2 m a}{g + a}$

Hence, the correct answer is option: 'A'.

Relevant Questions

The magnitude and direction of the acceleration produced in a body of mass kg when two mutually perpendicular forces N and N act on it, are 2026 (Cancelled)Newton's laws of motion
A uniform rod of mass 20 kg and length 5 m leans against a smooth vertical wall making an angle of with it. The other end rests on a rough h2025Newton's laws of motion
A horizontal force 10 N is applied to a block as shown in figure. The mass of blocks and are 2 kg and 3 kg respectively. The blocks slide ov2024Newton's laws of motion
A box of mass 5 kg is pulled by a cord, up along a frictionless plane inclined at with the horizontal. The tension in the cord is 30 N . The2024 (Re-NEET)Newton's laws of motion
Two bodies of mass 4 kg and 6 kg are tied to the ends of a massless string. The string passes over a pulley which is frictionless (see figur2020 (Phase 1)Newton's laws of motion
A block of mass m is placed on a smooth inclined wedge A B C of inclination as shown in the figure. The wedge is given an acceleration a tow2018Newton's laws of motion

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?

Solution

Relevant Questions

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 $a$ ?