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The magnitude of acceleration of blocks of mass 2kg and 4kg are a1 and a2 respectively. Considering pulley and strings are massless and g = 10 m/s2 , the relation between between a1 and a2 is i a1 = 2a2 ii 2a1 = a2 iii. a1 = 4a2 iv. a1 = a2?
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The magnitude of acceleration of blocks of mass 2kg and 4kg are a1 and...
**The Problem**
We are given two blocks with masses 2kg and 4kg respectively. The system consists of a pulley and two strings, which are assumed to be massless. The acceleration of the 2kg block is denoted as a1, and the acceleration of the 4kg block is denoted as a2. We are asked to determine the relation between a1 and a2.
**Analysis**
To solve this problem, we can apply Newton's second law of motion to each block individually and consider the tension in the strings.
**Newton's Second Law of Motion**
The second law of motion states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass:
F = ma
where F is the net force, m is the mass, and a is the acceleration.
**For the 2kg Block**
The net force acting on the 2kg block is the tension in the string pulling it upwards, minus the force of gravity pulling it downwards:
Tension - Weight = ma1
The weight of the block can be calculated as the product of its mass and the acceleration due to gravity (g = 10 m/s^2):
Tension - 2g = 2a1
**For the 4kg Block**
The net force acting on the 4kg block is the tension in the string pulling it downwards, plus the force of gravity pulling it downwards:
Tension + Weight = ma2
Again, the weight of the block can be calculated as the product of its mass and the acceleration due to gravity:
Tension + 4g = 4a2
**Solving for the Relation**
To determine the relation between a1 and a2, we can eliminate the tension from the equations by adding the two equations together:
(Tension - 2g) + (Tension + 4g) = 2a1 + 4a2
Simplifying the equation:
2Tension + 2g = 2(a1 + 2a2)
Since the pulley and strings are assumed to be massless, the tension in both strings is equal. Therefore, we can simplify further:
2Tension = 2(a1 + 2a2) - 2g
Cancelling out the 2 on both sides:
Tension = a1 + 2a2 - g
Now, we substitute this value of tension back into the equation for the 2kg block:
a1 + 2a2 - g - 2g = 2a1
Simplifying:
-3g = a1 - 2a2
Rearranging the equation:
a1 = 2a2 - 3g
Therefore, the relation between a1 and a2 is: a1 = 2a2 - 3g.
**Conclusion**
The correct relation between a1 and a2 is a1 = 2a2 - 3g. This shows that the acceleration of the 2kg block is equal to twice the acceleration of the 4kg block, minus three times the acceleration due to gravity.
We are given two blocks with masses 2kg and 4kg respectively. The system consists of a pulley and two strings, which are assumed to be massless. The acceleration of the 2kg block is denoted as a1, and the acceleration of the 4kg block is denoted as a2. We are asked to determine the relation between a1 and a2.
**Analysis**
To solve this problem, we can apply Newton's second law of motion to each block individually and consider the tension in the strings.
**Newton's Second Law of Motion**
The second law of motion states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass:
F = ma
where F is the net force, m is the mass, and a is the acceleration.
**For the 2kg Block**
The net force acting on the 2kg block is the tension in the string pulling it upwards, minus the force of gravity pulling it downwards:
Tension - Weight = ma1
The weight of the block can be calculated as the product of its mass and the acceleration due to gravity (g = 10 m/s^2):
Tension - 2g = 2a1
**For the 4kg Block**
The net force acting on the 4kg block is the tension in the string pulling it downwards, plus the force of gravity pulling it downwards:
Tension + Weight = ma2
Again, the weight of the block can be calculated as the product of its mass and the acceleration due to gravity:
Tension + 4g = 4a2
**Solving for the Relation**
To determine the relation between a1 and a2, we can eliminate the tension from the equations by adding the two equations together:
(Tension - 2g) + (Tension + 4g) = 2a1 + 4a2
Simplifying the equation:
2Tension + 2g = 2(a1 + 2a2)
Since the pulley and strings are assumed to be massless, the tension in both strings is equal. Therefore, we can simplify further:
2Tension = 2(a1 + 2a2) - 2g
Cancelling out the 2 on both sides:
Tension = a1 + 2a2 - g
Now, we substitute this value of tension back into the equation for the 2kg block:
a1 + 2a2 - g - 2g = 2a1
Simplifying:
-3g = a1 - 2a2
Rearranging the equation:
a1 = 2a2 - 3g
Therefore, the relation between a1 and a2 is: a1 = 2a2 - 3g.
**Conclusion**
The correct relation between a1 and a2 is a1 = 2a2 - 3g. This shows that the acceleration of the 2kg block is equal to twice the acceleration of the 4kg block, minus three times the acceleration due to gravity.
Community Answer
The magnitude of acceleration of blocks of mass 2kg and 4kg are a1 and...
D is the correct answer
bcoz as the pulley is massless n frictionless so tension in string will be same at all the points n hence acceleration of both the blocks would be same
bcoz as the pulley is massless n frictionless so tension in string will be same at all the points n hence acceleration of both the blocks would be same
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The magnitude of acceleration of blocks of mass 2kg and 4kg are a1 and a2 respectively. Considering pulley and strings are massless and g = 10 m/s2 , the relation between between a1 and a2 is i a1 = 2a2 ii 2a1 = a2 iii. a1 = 4a2 iv. a1 = a2?
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The magnitude of acceleration of blocks of mass 2kg and 4kg are a1 and a2 respectively. Considering pulley and strings are massless and g = 10 m/s2 , the relation between between a1 and a2 is i a1 = 2a2 ii 2a1 = a2 iii. a1 = 4a2 iv. a1 = a2? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about The magnitude of acceleration of blocks of mass 2kg and 4kg are a1 and a2 respectively. Considering pulley and strings are massless and g = 10 m/s2 , the relation between between a1 and a2 is i a1 = 2a2 ii 2a1 = a2 iii. a1 = 4a2 iv. a1 = a2? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The magnitude of acceleration of blocks of mass 2kg and 4kg are a1 and a2 respectively. Considering pulley and strings are massless and g = 10 m/s2 , the relation between between a1 and a2 is i a1 = 2a2 ii 2a1 = a2 iii. a1 = 4a2 iv. a1 = a2?.
The magnitude of acceleration of blocks of mass 2kg and 4kg are a1 and a2 respectively. Considering pulley and strings are massless and g = 10 m/s2 , the relation between between a1 and a2 is i a1 = 2a2 ii 2a1 = a2 iii. a1 = 4a2 iv. a1 = a2? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about The magnitude of acceleration of blocks of mass 2kg and 4kg are a1 and a2 respectively. Considering pulley and strings are massless and g = 10 m/s2 , the relation between between a1 and a2 is i a1 = 2a2 ii 2a1 = a2 iii. a1 = 4a2 iv. a1 = a2? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The magnitude of acceleration of blocks of mass 2kg and 4kg are a1 and a2 respectively. Considering pulley and strings are massless and g = 10 m/s2 , the relation between between a1 and a2 is i a1 = 2a2 ii 2a1 = a2 iii. a1 = 4a2 iv. a1 = a2?.
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The magnitude of acceleration of blocks of mass 2kg and 4kg are a1 and a2 respectively. Considering pulley and strings are massless and g = 10 m/s2 , the relation between between a1 and a2 is i a1 = 2a2 ii 2a1 = a2 iii. a1 = 4a2 iv. a1 = a2?, a detailed solution for The magnitude of acceleration of blocks of mass 2kg and 4kg are a1 and a2 respectively. Considering pulley and strings are massless and g = 10 m/s2 , the relation between between a1 and a2 is i a1 = 2a2 ii 2a1 = a2 iii. a1 = 4a2 iv. a1 = a2? has been provided alongside types of The magnitude of acceleration of blocks of mass 2kg and 4kg are a1 and a2 respectively. Considering pulley and strings are massless and g = 10 m/s2 , the relation between between a1 and a2 is i a1 = 2a2 ii 2a1 = a2 iii. a1 = 4a2 iv. a1 = a2? theory, EduRev gives you an
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