A balloon having mass 'm' is filled with gas and is held in hands of a boy. Then suddenly it gets released and gas starts coming out of it with a constant rate. The velocity of the ejected gas is `2m//s` with respect to the balloon. Find out the velocity of the balloon when the mass of gas is reduced to half :-

Options

A. `ln 2`
B. `2 ln 4`
C. `2 ln 2`
D. None of these

Answer

C

Explanation

`F_(ext) = m(dv)/(dt) + v_(rel) (dm)/(dt) rArr 0 = m (dv)/(dt) + 2 (dm)/(dt)`
`rArr -underset(+m)overset(m//2)int (2dm)/(m) = int_(0)^(v) dv rArr v = 2ln2`