A balloon of mass M is descending at a constant acceleration α 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 ?

Question

A balloon of mass M is descending at a constant acceleration α 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) (α/α+g)M (B) (2α/α+g)M (C) (α+g/α)M (D) (α+g/2 α)M

Tardigrade Admin · Accepted Answer

Suppose F = upthrust due to buoyancy Then while descending, we find Mg-F=M α ldots (i) when ascending, we have F-(M-m)g=(M-m) α ldots(ii) Solving equations (i) and (ii), we get: m=[(2α/α+g)]M

Q. A balloon of mass M is descending at a constant acceleration $α$ 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 ?

$\frac{α}{α + g} M$

$\frac{2 α}{α + g} M$

$\frac{α + g}{α} M$

$\frac{α + g}{2 α} M$

Suppose F = upthrust due to buoyancy

Then while descending, we find

$M g - F = M α \dots (i)$

when ascending, we have

$F - (M - m) g = (M - m) α \dots (ii)$

Solving equations (i) and (ii), we get:
$m = [\frac{2 α}{α + g}] M$

Q. A balloon of mass M is descending at a constant acceleration α 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 ?

α+gα​M

α+g2α​M

αα+g​M

2αα+g​M