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Q5.19: NCERT Physics - Part 1 WORK, ENERGY AND POWER 5.19 Solution: A trolley of mass 300 kg carrying a sandbag of 25 kg is moving…
⚠️ Common Exam Traps & Conceptual Pitfalls
Students often treat the trolley alone as an isolated system and apply $m v =\text{constant}$, expecting the speed to rise as mass drops. In reality the sand leaves with the same horizontal velocity as the trolley, so it carries away the exact horizontal momentum it had; the remaining trolley‑sand system experiences no net horizontal impulse and therefore keeps its original speed.
A trolley of mass 300 kg carrying a sandbag of 25 kg is moving uniformly with a speed of 27 km/h on a frictionless track. After a while, sand starts leaking out of a hole on the floor of the trolley at the rate of 0.05 kg s__. What is the speed of the trolley after the entire sand bag is empty?
Step-by-Step Verified Solution
**Answer:** Speed remains 27 km/h = 7.5 m/s.
**Step-by-Step Explanation:**
Since the track is frictionless and no external horizontal force acts, momentum is conserved.
The sand leaking out falls vertically and carries no horizontal momentum away from the trolley. The remaining system (trolley + remaining sand) continues with the same horizontal velocity.
Final speed = 27 km/h = 7.5 m/s.
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