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Blocks of mass m and 3m are attached to the two ends of a light inextensible string and passed over a light pulley. Find the acceleration of the lighter block(take g=10m/s^2)?
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Blocks of mass m and 3m are attached to the two ends of a light inexte...
Problem Statement: Two blocks of masses m and 3m are attached to the ends of a light inextensible string and passed over a light pulley. Find the acceleration of the lighter block (take g=10m/s^2).
Solution:
Step 1: Free Body Diagrams of the Blocks
The free body diagrams of the two blocks are shown below:
Step 2: Equations of Motion
Since the two blocks are connected by an inextensible string, the acceleration of both blocks is the same and can be represented by a.
Step 3: Elimination of Tension T
We can eliminate tension T by solving the two equations simultaneously.
Step 4: Final Answer
The acceleration of the lighter block is g/2 or 5 m/s^2.
Solution:
Step 1: Free Body Diagrams of the Blocks
The free body diagrams of the two blocks are shown below:
- Block of mass m: Tension T acts upward, Weight W = mg acts downward
- Block of mass 3m: Tension 3T acts upward, Weight W' = 3mg acts downward
Step 2: Equations of Motion
Since the two blocks are connected by an inextensible string, the acceleration of both blocks is the same and can be represented by a.
- For the block of mass m: T - mg = ma
- For the block of mass 3m: 3T - 3mg = 3ma
Step 3: Elimination of Tension T
We can eliminate tension T by solving the two equations simultaneously.
- From the first equation, T = ma + mg
- Substituting T in the second equation, we get: 3(ma + mg) - 3mg = 3ma
- Simplifying, we get: 2ma = mg
- Therefore, a = g/2
Step 4: Final Answer
The acceleration of the lighter block is g/2 or 5 m/s^2.
Community Answer
Blocks of mass m and 3m are attached to the two ends of a light inexte...
Suppose the mass 3m is on the right side of pulley and mass m is on the left side. Total force acting = 30-10N =20NThis force pulls the heavier mass 3m downwards and pulls the lighter mass m upwards. Since string and pulley is massless both will have same acceleration which is 20/(1+3) =5m/s^2
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Blocks of mass m and 3m are attached to the two ends of a light inextensible string and passed over a light pulley. Find the acceleration of the lighter block(take g=10m/s^2)?
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Blocks of mass m and 3m are attached to the two ends of a light inextensible string and passed over a light pulley. Find the acceleration of the lighter block(take g=10m/s^2)? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about Blocks of mass m and 3m are attached to the two ends of a light inextensible string and passed over a light pulley. Find the acceleration of the lighter block(take g=10m/s^2)? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Blocks of mass m and 3m are attached to the two ends of a light inextensible string and passed over a light pulley. Find the acceleration of the lighter block(take g=10m/s^2)?.
Blocks of mass m and 3m are attached to the two ends of a light inextensible string and passed over a light pulley. Find the acceleration of the lighter block(take g=10m/s^2)? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about Blocks of mass m and 3m are attached to the two ends of a light inextensible string and passed over a light pulley. Find the acceleration of the lighter block(take g=10m/s^2)? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Blocks of mass m and 3m are attached to the two ends of a light inextensible string and passed over a light pulley. Find the acceleration of the lighter block(take g=10m/s^2)?.
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