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The pulleys and strings shown in the figure are smooth and negligible mass for the system to remain in equilibrium the angle theta should be?
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The pulleys and strings shown in the figure are smooth and negligible ...
Analysis of Equilibrium in Pulley System
Given Data:
- Smooth pulleys and strings
- Negligible mass for pulleys and strings
Free Body Diagram:
- The forces acting on the 2 kg block are tension T and weight mg.
- The forces acting on the 3 kg block are tension 2T and weight 3g.
Equilibrium Condition:
- For the system to remain in equilibrium, the net force acting on each block must be zero.
- This can be achieved when the tensions in the strings are balanced by the weights of the blocks.
- Therefore, the tension T in the string supporting the 2 kg block must be equal to the weight of the 2 kg block (2g).
- Similarly, the tension 2T in the string supporting the 3 kg block must be equal to the weight of the 3 kg block (3g).
Relation between Tensions:
- Since the tensions in the strings are related to the weights of the blocks, we can write:
2T = 2g
T = g
2T = 3g
Calculation of Angle Theta:
- The angle theta can be calculated using trigonometry.
- sin(theta) = Opposite side / Hypotenuse
- sin(theta) = 2 / 3
- theta = sin^(-1)(2/3) = 41.81 degrees
Therefore, for the system to remain in equilibrium, the angle theta should be approximately 41.81 degrees.
Given Data:
- Smooth pulleys and strings
- Negligible mass for pulleys and strings
Free Body Diagram:
- The forces acting on the 2 kg block are tension T and weight mg.
- The forces acting on the 3 kg block are tension 2T and weight 3g.
Equilibrium Condition:
- For the system to remain in equilibrium, the net force acting on each block must be zero.
- This can be achieved when the tensions in the strings are balanced by the weights of the blocks.
- Therefore, the tension T in the string supporting the 2 kg block must be equal to the weight of the 2 kg block (2g).
- Similarly, the tension 2T in the string supporting the 3 kg block must be equal to the weight of the 3 kg block (3g).
Relation between Tensions:
- Since the tensions in the strings are related to the weights of the blocks, we can write:
2T = 2g
T = g
2T = 3g
Calculation of Angle Theta:
- The angle theta can be calculated using trigonometry.
- sin(theta) = Opposite side / Hypotenuse
- sin(theta) = 2 / 3
- theta = sin^(-1)(2/3) = 41.81 degrees
Therefore, for the system to remain in equilibrium, the angle theta should be approximately 41.81 degrees.
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The pulleys and strings shown in the figure are smooth and negligible mass for the system to remain in equilibrium the angle theta should be?
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The pulleys and strings shown in the figure are smooth and negligible mass for the system to remain in equilibrium the angle theta should be? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The pulleys and strings shown in the figure are smooth and negligible mass for the system to remain in equilibrium the angle theta should be? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The pulleys and strings shown in the figure are smooth and negligible mass for the system to remain in equilibrium the angle theta should be?.
The pulleys and strings shown in the figure are smooth and negligible mass for the system to remain in equilibrium the angle theta should be? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The pulleys and strings shown in the figure are smooth and negligible mass for the system to remain in equilibrium the angle theta should be? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The pulleys and strings shown in the figure are smooth and negligible mass for the system to remain in equilibrium the angle theta should be?.
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