A balloon with mass is descending down with an acceleration (where ). How much mass should be removed from it so that it starts moving up with an acceleration ? [2014]

STUDY MATERIALS
COURSES
MORE
SUCCESS STORY
ADMISSION
STORE

Back

JEE ADVANCE

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

JEE MAIN

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

NEET

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

BITSAT

CLASS XI - XII

CLASS XI - XII

CBSE BOARD

CLASS IX

CLASS X

CLASS XI

CLASS XII

CLASS VI

CLASS VII

CLASS VIII

UP BOARD

CLASS IX
CLASS X
CLASS XI
CLASS XII

CLASS IX

CLASS X

CLASS XI

CLASS XII

CUET

CRASH COURSE

CRASH COURSE

Courses

CLASSROOM COURSES
ONLINE COURSES

ONLINE COURSES

More

Solution

Q.
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 $a$ [2014]

1 $\frac{2 m a}{g + a}$

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

3 $\frac{m a}{g + a}$

4 $\frac{m a}{g - a}$

Ans.
(1)

Let $F$ be the upthrust of the air. As the balloon is descending down with an acceleration $a$ ,

$∴$    $m g - F = m a$ ...(i)

Let mass $m_{0}$ be removed from the balloon so that it starts moving up with an acceleration $a$ . Then,

$F - (m - m_{0}) g = (m - m_{0}) a$

$F - m g + m_{0} g = m a - m_{0} a$ ...(ii)

Adding equation (i) and equation (ii), we get

   $m_{0} g = 2 m a - m_{0} a;$ $m_{0} g + m_{0} a = 2 m a$

   $m_{0} (g + a) = 2 m a$

   $m_{0} = \frac{2 m a}{a + g}$

Want Us to Email you About Special Offers & Updates?