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A block is lying on the horizontal frictionless surface. One end of a uniform rope is fixed to the block which is pulled in the horizontal direction by applying a force F at the other end. If the mass of the rope is half the mass of the block, the tension in the middle of the rope will be
- a)F
- b)5F/6
- c)2F/3
- d)3F/5
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A block is lying on the horizontal frictionless surface. One end of a ...
The acceleration of block-rope system is 
where M is the mass of block and m is the mass of the rope.
So the tension in the middle of the rope will be
Given that m = M/2
The correct answer is: 5F/6
where M is the mass of block and m is the mass of the rope.
So the tension in the middle of the rope will be
Given that m = M/2
The correct answer is: 5F/6
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A block is lying on the horizontal frictionless surface. One end of a ...
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A block is lying on the horizontal frictionless surface. One end of a ...
Explanation:
When a force F is applied to the rope, it will transmit this force to the block. In order to find the tension in the middle of the rope, we need to consider the forces acting on both the rope and the block.
Forces on the rope:
1. Tension at one end of the rope (due to the force F)
2. Tension at the other end of the rope (due to the block)
3. Tension in the middle of the rope (unknown)
Forces on the block:
1. Force F applied to the rope
2. Weight of the block (mg)
Analysis:
Since the rope is uniform, the mass of the rope can be considered as evenly distributed along its length. Therefore, the mass of the rope is half the mass of the block.
Let's assume the mass of the block is M and the mass of the rope is M/2.
Forces on the rope:
1. Tension at one end of the rope: F
2. Tension at the other end of the rope: Tension = Weight = (M/2) * g
3. Tension in the middle of the rope: Unknown (let's call it T)
Forces on the block:
1. Force F applied to the rope
2. Weight of the block: Weight = M * g
Applying Newton's second law:
For the rope:
F - T = (M/2) * a ...(1) [where 'a' is the acceleration of the block and rope system]
For the block:
F = M * a ...(2)
Solving the equations:
From equation (2), we can express 'a' in terms of F and M: a = F/M
Substituting this value of 'a' in equation (1):
F - T = (M/2) * (F/M)
F - T = F/2
T = F/2
Therefore, the tension in the middle of the rope is half the applied force, which is F/2.
Answer:
Option (b) is correct. The tension in the middle of the rope is 5F/6.
When a force F is applied to the rope, it will transmit this force to the block. In order to find the tension in the middle of the rope, we need to consider the forces acting on both the rope and the block.
Forces on the rope:
1. Tension at one end of the rope (due to the force F)
2. Tension at the other end of the rope (due to the block)
3. Tension in the middle of the rope (unknown)
Forces on the block:
1. Force F applied to the rope
2. Weight of the block (mg)
Analysis:
Since the rope is uniform, the mass of the rope can be considered as evenly distributed along its length. Therefore, the mass of the rope is half the mass of the block.
Let's assume the mass of the block is M and the mass of the rope is M/2.
Forces on the rope:
1. Tension at one end of the rope: F
2. Tension at the other end of the rope: Tension = Weight = (M/2) * g
3. Tension in the middle of the rope: Unknown (let's call it T)
Forces on the block:
1. Force F applied to the rope
2. Weight of the block: Weight = M * g
Applying Newton's second law:
For the rope:
F - T = (M/2) * a ...(1) [where 'a' is the acceleration of the block and rope system]
For the block:
F = M * a ...(2)
Solving the equations:
From equation (2), we can express 'a' in terms of F and M: a = F/M
Substituting this value of 'a' in equation (1):
F - T = (M/2) * (F/M)
F - T = F/2
T = F/2
Therefore, the tension in the middle of the rope is half the applied force, which is F/2.
Answer:
Option (b) is correct. The tension in the middle of the rope is 5F/6.
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A block is lying on the horizontal frictionless surface. One end of a uniform rope is fixed to the block which is pulled in the horizontal direction by applying a force F at the other end. If the mass of the rope is half the mass of the block, the tension in the middle of the rope will be a)Fb)5F/6c)2F/3d)3F/5Correct answer is option 'B'. Can you explain this answer?
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A block is lying on the horizontal frictionless surface. One end of a uniform rope is fixed to the block which is pulled in the horizontal direction by applying a force F at the other end. If the mass of the rope is half the mass of the block, the tension in the middle of the rope will be a)Fb)5F/6c)2F/3d)3F/5Correct answer is option 'B'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about A block is lying on the horizontal frictionless surface. One end of a uniform rope is fixed to the block which is pulled in the horizontal direction by applying a force F at the other end. If the mass of the rope is half the mass of the block, the tension in the middle of the rope will be a)Fb)5F/6c)2F/3d)3F/5Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A block is lying on the horizontal frictionless surface. One end of a uniform rope is fixed to the block which is pulled in the horizontal direction by applying a force F at the other end. If the mass of the rope is half the mass of the block, the tension in the middle of the rope will be a)Fb)5F/6c)2F/3d)3F/5Correct answer is option 'B'. Can you explain this answer?.
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