Question

A hot air balloon loaded with sandbags has a total mass of M. It is descending with a downward acceleration of g/2, where g is the acceleration of free fall. How much sand must be released from the sandbags in order that hot air balloon ascends with the same acceleration?

Answer 1

Consider upthrust that will take the balloon upward in normal course to be 'T'

By the first condition,

Mg - T = M(g/2) ------- (i)

Let 'm' be mass of sand taken out/ released so that the balloon starts moving upwards with acceleration (g/2). Then mass of the hot air balloon is ( M - m ). In such situation, we have

T - ( M - m )g = ( M - m ) (g/2) ------ (ii)

Adding (i) and (ii), we get

Mg - ( M - m )g = Mg/2 + ( M - m  )g/2

=> mg = Mg - mg/2

=> mg + mg/2 = Mg

=> 3mg/2 = Mg

=> m = 2M/3