A hot air ballon of mass M is descending vertically downward with acceleration a. How much mass must be removed to give ballon an upward acceleration of a?

Question

A hot air ballon of mass M is descending vertically downward with acceleration a. How much mass must be removed to give ballon an upward acceleration of a? (A) (Ma/(g+a)) (B) (Ma/(g-a)) (C) (2Ma/(g+a)) (D) (2Ma/(g- a))

Tardigrade Admin · Accepted Answer

Let F be constant upthrust force and m is the removed mass. Free body diagram for case (1).

(Mg - F) = Ma ...(i) Free body digram for case (2)

F - (M -m)g = (M -m )a ...(ii) Adding (i) and (ii), we get mg = 2 Ma - ma m(g + a) = 2 Ma m = (2Ma/(g+a))

Q. A hot air ballon of mass $M$ is descending vertically downward with acceleration $a$ . How much mass must be removed to give ballon an upward acceleration of $a$ ?

$\frac{M a}{( g + a )}$

$\frac{M a}{( g - a )}$

$\frac{2 M a}{( g + a )}$

$\frac{2 M a}{( g - a )}$

Let $F$ be constant upthrust force and $m$ is the removed mass.
Free body diagram for case $(1)$ .

$(M g - F) = M a ... (i)$
Free body digram for case $(2)$

$F - (M - m) g = (M - m) a ... (ii)$
Adding $(i)$ and $(ii)$ , we get
$m g = 2 M a - ma$
$m (g + a) = 2 M a$
$m = \frac{2 M a}{( g + a )}$

Q. A hot air ballon of mass M is descending vertically downward with acceleration a. How much mass must be removed to give ballon an upward acceleration of a?

(g+a)Ma​

(g−a)Ma​

(g+a)2Ma​

(g−a)2Ma​