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A wagon 1000 kg is moving with a velocity 50 km/h on smooth horizontal rails. A mass of 250 kg is dropped into it. The velocity with which it moves now is
- a)12.5 km/hour
- b)20 km/hour
- c)40 km/hour
- d)50 km/hour
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A wagon 1000 kg is moving with a velocity 50 km/h on smooth horizontal...
m1u = m2v
1000 x 50 = (1000 + 250) ν, ν = 40 km / hr.
1000 x 50 = (1000 + 250) ν, ν = 40 km / hr.
Most Upvoted Answer
A wagon 1000 kg is moving with a velocity 50 km/h on smooth horizontal...
Understanding the Problem
To find the new velocity of the wagon after the mass is dropped into it, we can apply the principle of conservation of momentum. The total momentum before and after the mass is dropped must remain constant, as no external horizontal forces are acting on the wagon.
Given Data
- Mass of the wagon (m1) = 1000 kg
- Initial velocity of the wagon (v1) = 50 km/h
- Mass dropped (m2) = 250 kg
- Final velocity after dropping (v2) = ?
Converting Units
First, we need to convert the velocity from km/h to m/s for easier calculations:
- 50 km/h = (50 * 1000) / 3600 = 13.89 m/s
Applying Conservation of Momentum
The initial momentum (p_initial) can be calculated as:
- p_initial = m1 * v1 = 1000 kg * 13.89 m/s = 13889 kg·m/s
After the mass is dropped, the total mass (m_total) becomes:
- m_total = m1 + m2 = 1000 kg + 250 kg = 1250 kg
Let v2 be the final velocity of the wagon. The final momentum (p_final) is:
- p_final = m_total * v2 = 1250 kg * v2
According to the conservation of momentum:
- p_initial = p_final
Setting up the Equation
- 13889 kg·m/s = 1250 kg * v2
Now, solve for v2:
- v2 = 13889 kg·m/s / 1250 kg = 11.11 m/s
Converting Back to km/h
Finally, convert v2 back to km/h:
- v2 = 11.11 m/s * (3600 / 1000) = 40 km/h
Conclusion
The new velocity of the wagon after the mass is dropped into it is 40 km/h. Therefore, the correct answer is option C.
To find the new velocity of the wagon after the mass is dropped into it, we can apply the principle of conservation of momentum. The total momentum before and after the mass is dropped must remain constant, as no external horizontal forces are acting on the wagon.
Given Data
- Mass of the wagon (m1) = 1000 kg
- Initial velocity of the wagon (v1) = 50 km/h
- Mass dropped (m2) = 250 kg
- Final velocity after dropping (v2) = ?
Converting Units
First, we need to convert the velocity from km/h to m/s for easier calculations:
- 50 km/h = (50 * 1000) / 3600 = 13.89 m/s
Applying Conservation of Momentum
The initial momentum (p_initial) can be calculated as:
- p_initial = m1 * v1 = 1000 kg * 13.89 m/s = 13889 kg·m/s
After the mass is dropped, the total mass (m_total) becomes:
- m_total = m1 + m2 = 1000 kg + 250 kg = 1250 kg
Let v2 be the final velocity of the wagon. The final momentum (p_final) is:
- p_final = m_total * v2 = 1250 kg * v2
According to the conservation of momentum:
- p_initial = p_final
Setting up the Equation
- 13889 kg·m/s = 1250 kg * v2
Now, solve for v2:
- v2 = 13889 kg·m/s / 1250 kg = 11.11 m/s
Converting Back to km/h
Finally, convert v2 back to km/h:
- v2 = 11.11 m/s * (3600 / 1000) = 40 km/h
Conclusion
The new velocity of the wagon after the mass is dropped into it is 40 km/h. Therefore, the correct answer is option C.
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A wagon 1000 kg is moving with a velocity 50 km/h on smooth horizontal rails. A mass of 250 kg is dropped into it. The velocity with which it moves now isa)12.5 km/hourb)20 km/hourc)40 km/hourd)50 km/hourCorrect answer is option 'C'. Can you explain this answer?
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A wagon 1000 kg is moving with a velocity 50 km/h on smooth horizontal rails. A mass of 250 kg is dropped into it. The velocity with which it moves now isa)12.5 km/hourb)20 km/hourc)40 km/hourd)50 km/hourCorrect answer is option 'C'. Can you explain this answer? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A wagon 1000 kg is moving with a velocity 50 km/h on smooth horizontal rails. A mass of 250 kg is dropped into it. The velocity with which it moves now isa)12.5 km/hourb)20 km/hourc)40 km/hourd)50 km/hourCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A wagon 1000 kg is moving with a velocity 50 km/h on smooth horizontal rails. A mass of 250 kg is dropped into it. The velocity with which it moves now isa)12.5 km/hourb)20 km/hourc)40 km/hourd)50 km/hourCorrect answer is option 'C'. Can you explain this answer?.
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