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A cannon and a supply of cannon balls are inside a sealed rail road car at rest. The cannon fires to the right, the car recoils to the left. The balls remain in the car after hitting the farther wall. Assume friction to be absent. If L is the length of the rail road car, D is the distance traversed by the rail road car relative to the ground, m is the total mass of cannon balls fired and M is the total mass of remaining system (cannon + car) then

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$D = \frac{M L}{M + m}$

$D < L$

$D = \frac{m L}{M + m}$

answer is B, D.

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Detailed Solution

$\Rightarrow Δ x_{c m} = \frac{m Δ x_{1} + M Δ x_{2}}{M + m} = 0$

$\Rightarrow m Δ x_{3} + M Δ x_{2} = 0$

$\Rightarrow m (L - D) + M D = 0$

$\Rightarrow D = \frac{m L}{M + m} < L$

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