Q 11-04-068JEE MainJEE Main 2025 (28 Jan, Shift 2)Medium
A balloon and its content having mass $M$ is moving up with an acceleration $a$. The mass that must be released from the content so that the balloon starts moving up with an acceleration $3a$ will be (Take $g$ as acceleration due to gravity)
Answer: (A) $\dfrac{2Ma}{3a+g}$
The upthrust $U$ stays the same.
Initially: $U - Mg = Ma \Rightarrow U = M(g + a)$.
After releasing mass $m$: $U - (M - m)g = (M - m)3a$
$$M(g + a) = (M - m)(g + 3a) \Rightarrow m(g + 3a) = 2Ma \Rightarrow m = \frac{2Ma}{3a + g}$$
Solution by Sreeraj P, M.Sc Physics