A balloon of mass M, carrying some is descending with an acceleration a. When `(1)/(4)` th of the sand is emptied out the balloon, the balloon descends with a unifrom velocity. Find the initial mass of sand in the balloon.

Explanation

Let the initial mass of sand in the balloon be m and the upward thrust of air on the balloon or air resistance be F. Hence, the equation of motion initially is,
(M + m ) g - F = (M + m)a …(1)
After `(1)/(4)` th of the sand is emptied out, the equation changes to
`[ M + ( m - (m)/(4)) ] g - F = 0` ....(2)
From (1) and (2) ,
`( M + m) g - [M + (m - (m)/(4)) ] g = (M + m)a`
or, `" " (m)/(4) g = (M + m)a `
or, `" " m = (Ma)/(((1)/(4)g - a )) = (4Ma)/(g - 4a)`