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A balloon of mass 'm' is filled with gas and held by a boy. It is suddenly released and gas escapes at a constant rate, the exhaust speed being a constant 2 m/s relative to the balloon. Neglecting gravity, find the speed of the balloon when its (gas) mass has dropped to half.

1. ln 2
2. 2 ln 4
3. 2 ln 2
4. none of these

Correct answer: 2 ln 2

Solution

By the rocket equation with no gravity, v = u ln(m_i/m_f) = 2 * ln(2) = 2 ln 2 m/s.

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