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A massless string passes over a frictionless pulley and carries two masses
m, and m₂(m, m,) at its ends. If g is the acceleration due to gravity, then the thrust on the
pulley is (m,>m₁)?
m, and m₂(m, m,) at its ends. If g is the acceleration due to gravity, then the thrust on the
pulley is (m,>m₁)?
Most Upvoted Answer
A massless string passes over a frictionless pulley and carries two ma...
- **Analysis of the problem**
- **Free body diagrams of the masses**
Let's consider the free body diagrams of the masses m₁ and m₂. For mass m₁, the forces acting are tension T₁ acting upwards and weight mg acting downwards. Therefore, the net force on mass m₁ is given by:
m₁g - T₁ = m₁a
For mass m₂, the forces acting are tension T₂ acting upwards and weight 2mg acting downwards (as m₂ = 2m). Therefore, the net force on mass m₂ is given by:
2mg - T₂ = 2ma
- **Relation between T₁ and T₂**
Since the string is massless and frictionless, the tension in the string is constant throughout. Therefore, T₁ = T₂ = T (say).
- **Thrust on the pulley**
The net force acting on the pulley is the difference between the tensions on either side of the pulley. Therefore, the thrust on the pulley is given by:
Thrust = T₂ - T₁ = 2mg - m₁g = (2m - m₁)g
- **Conclusion**
The thrust on the pulley is proportional to the difference in the masses attached to the string. In this case, if m₂ > m₁, then the thrust on the pulley will be greater than if m₁ > m₂.
- **Free body diagrams of the masses**
Let's consider the free body diagrams of the masses m₁ and m₂. For mass m₁, the forces acting are tension T₁ acting upwards and weight mg acting downwards. Therefore, the net force on mass m₁ is given by:
m₁g - T₁ = m₁a
For mass m₂, the forces acting are tension T₂ acting upwards and weight 2mg acting downwards (as m₂ = 2m). Therefore, the net force on mass m₂ is given by:
2mg - T₂ = 2ma
- **Relation between T₁ and T₂**
Since the string is massless and frictionless, the tension in the string is constant throughout. Therefore, T₁ = T₂ = T (say).
- **Thrust on the pulley**
The net force acting on the pulley is the difference between the tensions on either side of the pulley. Therefore, the thrust on the pulley is given by:
Thrust = T₂ - T₁ = 2mg - m₁g = (2m - m₁)g
- **Conclusion**
The thrust on the pulley is proportional to the difference in the masses attached to the string. In this case, if m₂ > m₁, then the thrust on the pulley will be greater than if m₁ > m₂.
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A massless string passes over a frictionless pulley and carries two massesm, and m₂(m, m,) at its ends. If g is the acceleration due to gravity, then the thrust on thepulley is (m,>m₁)?
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A massless string passes over a frictionless pulley and carries two massesm, and m₂(m, m,) at its ends. If g is the acceleration due to gravity, then the thrust on thepulley is (m,>m₁)? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A massless string passes over a frictionless pulley and carries two massesm, and m₂(m, m,) at its ends. If g is the acceleration due to gravity, then the thrust on thepulley is (m,>m₁)? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A massless string passes over a frictionless pulley and carries two massesm, and m₂(m, m,) at its ends. If g is the acceleration due to gravity, then the thrust on thepulley is (m,>m₁)?.
A massless string passes over a frictionless pulley and carries two massesm, and m₂(m, m,) at its ends. If g is the acceleration due to gravity, then the thrust on thepulley is (m,>m₁)? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A massless string passes over a frictionless pulley and carries two massesm, and m₂(m, m,) at its ends. If g is the acceleration due to gravity, then the thrust on thepulley is (m,>m₁)? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A massless string passes over a frictionless pulley and carries two massesm, and m₂(m, m,) at its ends. If g is the acceleration due to gravity, then the thrust on thepulley is (m,>m₁)?.
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