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Two wires P and Q of same length and material but radii in the ratio 2 : 1 are suspended from a rigid support. Find the ratio of strain produced in the wires when both are under same force.
- a)1:2
- b)4:1
- c)1:4
- d)2:1
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Two wires P and Q of same length and material but radii in the ratio 2...
Using Hooke ‘s Law we get
Stress directly proportional to stress = Load/Area=F/pie*r*r
And rp:rq=2:1
When both the wires are under the same stress,strain produced will be the same.
When both the wires are under the same stress,strain produced will be the same.
2.when both the wires are loaded by same weight then
Strain p/strain q=(rq)2/(rp)2=¼
Most Upvoted Answer
Two wires P and Q of same length and material but radii in the ratio 2...
Given:
- Two wires P and Q of same length and material
- Radii of wires P and Q are in the ratio 2:1
To find:
- Ratio of strain produced in the wires when both are under the same force
Strain is defined as the ratio of change in length to the original length of a wire. It is given by the formula:
Strain = change in length / original length
Let's assume the original length of both wires P and Q is L.
The change in length of a wire is directly proportional to the force applied and inversely proportional to the cross-sectional area of the wire. Mathematically, it can be expressed as:
Change in length ∝ Force / Cross-sectional area
As both wires are made of the same material, the Young's modulus (a measure of stiffness) is the same for both wires.
Let's calculate the cross-sectional area of wire P and wire Q:
- Let the radius of wire P be 2r
- Therefore, the radius of wire Q will be r (as per the given ratio)
- The cross-sectional area of wire P = π(2r)^2 = 4πr^2
- The cross-sectional area of wire Q = π(r)^2 = πr^2
Now, let's consider the force applied to both wires to be F.
The change in length of wire P can be calculated using the formula:
Change in length of wire P = (F * L) / (4πr^2 * Y) ... (1)
where Y is the Young's modulus of the material.
Similarly, the change in length of wire Q can be calculated using the formula:
Change in length of wire Q = (F * L) / (πr^2 * Y) ... (2)
Taking the ratio of equation (1) and equation (2), we get:
Strain in wire P / Strain in wire Q = [(F * L) / (4πr^2 * Y)] / [(F * L) / (πr^2 * Y)]
= [(F * L) / (4πr^2 * Y)] * [(πr^2 * Y) / (F * L)]
= 1/4
Therefore, the ratio of strain produced in wire P to wire Q is 1:4.
Hence, the correct answer is option (c) 1:4.
- Two wires P and Q of same length and material
- Radii of wires P and Q are in the ratio 2:1
To find:
- Ratio of strain produced in the wires when both are under the same force
Strain is defined as the ratio of change in length to the original length of a wire. It is given by the formula:
Strain = change in length / original length
Let's assume the original length of both wires P and Q is L.
The change in length of a wire is directly proportional to the force applied and inversely proportional to the cross-sectional area of the wire. Mathematically, it can be expressed as:
Change in length ∝ Force / Cross-sectional area
As both wires are made of the same material, the Young's modulus (a measure of stiffness) is the same for both wires.
Let's calculate the cross-sectional area of wire P and wire Q:
- Let the radius of wire P be 2r
- Therefore, the radius of wire Q will be r (as per the given ratio)
- The cross-sectional area of wire P = π(2r)^2 = 4πr^2
- The cross-sectional area of wire Q = π(r)^2 = πr^2
Now, let's consider the force applied to both wires to be F.
The change in length of wire P can be calculated using the formula:
Change in length of wire P = (F * L) / (4πr^2 * Y) ... (1)
where Y is the Young's modulus of the material.
Similarly, the change in length of wire Q can be calculated using the formula:
Change in length of wire Q = (F * L) / (πr^2 * Y) ... (2)
Taking the ratio of equation (1) and equation (2), we get:
Strain in wire P / Strain in wire Q = [(F * L) / (4πr^2 * Y)] / [(F * L) / (πr^2 * Y)]
= [(F * L) / (4πr^2 * Y)] * [(πr^2 * Y) / (F * L)]
= 1/4
Therefore, the ratio of strain produced in wire P to wire Q is 1:4.
Hence, the correct answer is option (c) 1:4.
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Two wires P and Q of same length and material but radii in the ratio 2 : 1 are suspended from a rigid support. Find the ratio of strain produced in the wires when both are under same force.a)1:2b)4:1c)1:4d)2:1Correct answer is option 'C'. Can you explain this answer?
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Two wires P and Q of same length and material but radii in the ratio 2 : 1 are suspended from a rigid support. Find the ratio of strain produced in the wires when both are under same force.a)1:2b)4:1c)1:4d)2:1Correct answer is option 'C'. Can you explain this answer? for Class 11 2025 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about Two wires P and Q of same length and material but radii in the ratio 2 : 1 are suspended from a rigid support. Find the ratio of strain produced in the wires when both are under same force.a)1:2b)4:1c)1:4d)2:1Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 11 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two wires P and Q of same length and material but radii in the ratio 2 : 1 are suspended from a rigid support. Find the ratio of strain produced in the wires when both are under same force.a)1:2b)4:1c)1:4d)2:1Correct answer is option 'C'. Can you explain this answer?.
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Two wires P and Q of same length and material but radii in the ratio 2 : 1 are suspended from a rigid support. Find the ratio of strain produced in the wires when both are under same force.a)1:2b)4:1c)1:4d)2:1Correct answer is option 'C'. Can you explain this answer?, a detailed solution for Two wires P and Q of same length and material but radii in the ratio 2 : 1 are suspended from a rigid support. Find the ratio of strain produced in the wires when both are under same force.a)1:2b)4:1c)1:4d)2:1Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of Two wires P and Q of same length and material but radii in the ratio 2 : 1 are suspended from a rigid support. Find the ratio of strain produced in the wires when both are under same force.a)1:2b)4:1c)1:4d)2:1Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
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