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Two blocks of masses m and M are connected by means of metal wire of cross section area A passing over a frictionless pulley the system is then released if M=2m then tension per unit crossectional area produce in wire?
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Two blocks of masses m and M are connected by means of metal wire of c...
Problem: Two blocks of masses m and M are connected by means of metal wire of cross section area A passing over a frictionless pulley the system is then released if M=2m then tension per unit crossectional area produce in wire?
Solution:
First, draw the free body diagram of the system. The diagram will consist of two blocks, one pulley, and the wire connecting them. Assign the direction of motion for both the blocks.
Apply Newton's Second Law of Motion to both the blocks. Since the pulley is frictionless, there is no force acting on it. Therefore, the tension in the wire will be the same on both sides of the pulley.
Let T be the tension in the wire. Then, the equations of motion for the two blocks are:
mgsinθ - T = ma (1)
T - Mg = Ma (2)
where θ is the angle of inclination of the plane.
Substituting M=2m in equation (2), we get:
T - 2mg = 2ma
From equation (1), we get:
T = mgsinθ + ma
Substituting a from equation (2), we get:
T = mgsinθ + (T - 2mg)/2
Simplifying the equation, we get:
T = 2mgsinθ/3
Therefore, the tension per unit cross-sectional area produced in the wire is:
T/A = (2mgsinθ/3)/A
Thus, the tension per unit cross-sectional area produced in the wire is (2mgsinθ/3)/A.
Solution:
Step 1: Free body diagram
First, draw the free body diagram of the system. The diagram will consist of two blocks, one pulley, and the wire connecting them. Assign the direction of motion for both the blocks.
Step 2: Applying Newton's Second Law
Apply Newton's Second Law of Motion to both the blocks. Since the pulley is frictionless, there is no force acting on it. Therefore, the tension in the wire will be the same on both sides of the pulley.
Step 3: Solving for Tension
Let T be the tension in the wire. Then, the equations of motion for the two blocks are:
mgsinθ - T = ma (1)
T - Mg = Ma (2)
where θ is the angle of inclination of the plane.
Substituting M=2m in equation (2), we get:
T - 2mg = 2ma
From equation (1), we get:
T = mgsinθ + ma
Substituting a from equation (2), we get:
T = mgsinθ + (T - 2mg)/2
Simplifying the equation, we get:
T = 2mgsinθ/3
Therefore, the tension per unit cross-sectional area produced in the wire is:
T/A = (2mgsinθ/3)/A
Step 4: Final Answer
Thus, the tension per unit cross-sectional area produced in the wire is (2mgsinθ/3)/A.
Community Answer
Two blocks of masses m and M are connected by means of metal wire of c...
Given that pulley is frictioness. So heavy block i.e M=2m moves downwards let with acceleration 'a' and lighter block m moves upwards with same acceleration . So the equation of these two blocks become
T- mg=ma
&. 2mg-T =2ma
Adding both the equations we get ,
mg=3ma or a=g/3
Putting the value of 'a' in any of above equation,we get tension T= mg/3+mg=4mg/3.
We know that T remain same everywhere in the wire if the wire used is single or same.
T- mg=ma
&. 2mg-T =2ma
Adding both the equations we get ,
mg=3ma or a=g/3
Putting the value of 'a' in any of above equation,we get tension T= mg/3+mg=4mg/3.
We know that T remain same everywhere in the wire if the wire used is single or same.
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Two blocks of masses m and M are connected by means of metal wire of cross section area A passing over a frictionless pulley the system is then released if M=2m then tension per unit crossectional area produce in wire?
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Two blocks of masses m and M are connected by means of metal wire of cross section area A passing over a frictionless pulley the system is then released if M=2m then tension per unit crossectional area produce in wire? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Two blocks of masses m and M are connected by means of metal wire of cross section area A passing over a frictionless pulley the system is then released if M=2m then tension per unit crossectional area produce in wire? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two blocks of masses m and M are connected by means of metal wire of cross section area A passing over a frictionless pulley the system is then released if M=2m then tension per unit crossectional area produce in wire?.
Two blocks of masses m and M are connected by means of metal wire of cross section area A passing over a frictionless pulley the system is then released if M=2m then tension per unit crossectional area produce in wire? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Two blocks of masses m and M are connected by means of metal wire of cross section area A passing over a frictionless pulley the system is then released if M=2m then tension per unit crossectional area produce in wire? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two blocks of masses m and M are connected by means of metal wire of cross section area A passing over a frictionless pulley the system is then released if M=2m then tension per unit crossectional area produce in wire?.
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