Question

A balloon having mass 'm' is filled with gas and is held in hands of a boy. Then suddenly it get released and gas starts coming out of it with a constant rate of 2 m/s with respect to the balloon. Find out the velocity of the balloon when the mass of gas is reduced to half. (Neglect gravity & Buoyant force).

• A. ln 2
• B. 2 ln 4
• C. 2 ln2
• D. none of these

Answer 1

The correct option is C 2 ln2

Thrust force $F_t=-v_r\frac{dm}{dt}$ , where $v_r=2m/s$

Now this force will accelerate balloon . Also mass will change from m to $m/2$

So $F_t=ma$

$-v_r\frac{dm}{dt}=m\frac{dv}{dt}$

$-2{\int }_m^{m/2}\frac{dm}{m}={\int }_o^{v}dv$

so $v=2ln2$