A cart sliding with speed v on a frictionless track starts leaking sand. Does the cart's
speed (i) increase (ii) decrease (iii) remains the same? Explain.
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Answer: The speed increases.
Explanation: In accordance with the principle of conservation of linear momentum, the momentum of a body on which no net external force acts is conserved, i.e., it remains constant.
When such a body loses mass by any means, to compensate for the loss in momentum(since p=mv), the velocity increases proportionally. In your case, the cart loses it's mass, but it's momentum is conserved which means its velocity MUST INCREASE to conserve momentum.
Fun fact: The same principle is used to accelerate space probes into deep space; they shed payload to acquire greater velocity(since the forces acting in free space are generally negligible).
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