Question

A balloon of mass M is descending at a constant acceleration a. When a mass m is released from the balloon it starts rising with the same acceleration ‘a’. Assuming that its volume does not change, what is the value of m?

• A. $\frac{\alpha}{\alpha + g}M$
• B. $\frac{2\alpha}{\alpha + g}M$
• C. $\frac{\alpha + g}{\alpha}M$
• D. $\frac{\alpha + g}{2\alpha}M$

Answer 1

Answer: (B)

$\frac{2\alpha}{\alpha + g}M$

Answer 2

When balloon is descending, Mg – F_b = M

 F_b = Mg – M ..….(1)

When balloon is ascending, F_b – (M – m)g

= (M – m) ……(2)

from these two equations, m = $\frac{2\alpha M}{\alpha + g}$