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The ratio of the lengths of two wires A and B of the same material is 1: 2, and the ratio of their diameter is 2: 1. They are stretched by the same force, then the ratio of increase in length will be
- a)2:1
- b)1:2
- c)1:8
- d)1:4
Correct answer is option 'C'. Can you explain this answer?
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The ratio of the lengths of two wires A and B of the same material is...
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The ratio of the lengths of two wires A and B of the same material is...
Given information:
Length ratio of wire A to wire B = 1:2
Diameter ratio of wire A to wire B = 2:1
To find:
Ratio of increase in length
Analysis:
When a wire is stretched by a force, it undergoes an increase in length. This increase in length is directly proportional to the applied force and inversely proportional to the cross-sectional area of the wire. In other words, if two wires of the same material and different dimensions are stretched by the same force, the wire with a smaller cross-sectional area will experience a greater increase in length.
Let's consider wire A and wire B:
Length ratio of wire A to wire B = 1:2
This means that if the original length of wire A is represented by 'x', the original length of wire B will be '2x'.
Diameter ratio of wire A to wire B = 2:1
This means that if the diameter of wire A is represented by '2d', the diameter of wire B will be 'd' (where 'd' is a constant).
Calculations:
To compare the increase in length of wire A and wire B, we need to consider their cross-sectional areas. The cross-sectional area of a wire is directly proportional to the square of its diameter.
Cross-sectional area of wire A = π(2d)^2 = 4πd^2
Cross-sectional area of wire B = πd^2
Ratio of cross-sectional areas = (4πd^2) / (πd^2) = 4:1
Since the force applied is the same for both wires, the increase in length is inversely proportional to their cross-sectional areas.
Ratio of increase in length = 1:4 (inverse of 4:1) = 1:4
Therefore, the correct answer is option C) 1:8
Length ratio of wire A to wire B = 1:2
Diameter ratio of wire A to wire B = 2:1
To find:
Ratio of increase in length
Analysis:
When a wire is stretched by a force, it undergoes an increase in length. This increase in length is directly proportional to the applied force and inversely proportional to the cross-sectional area of the wire. In other words, if two wires of the same material and different dimensions are stretched by the same force, the wire with a smaller cross-sectional area will experience a greater increase in length.
Let's consider wire A and wire B:
Length ratio of wire A to wire B = 1:2
This means that if the original length of wire A is represented by 'x', the original length of wire B will be '2x'.
Diameter ratio of wire A to wire B = 2:1
This means that if the diameter of wire A is represented by '2d', the diameter of wire B will be 'd' (where 'd' is a constant).
Calculations:
To compare the increase in length of wire A and wire B, we need to consider their cross-sectional areas. The cross-sectional area of a wire is directly proportional to the square of its diameter.
Cross-sectional area of wire A = π(2d)^2 = 4πd^2
Cross-sectional area of wire B = πd^2
Ratio of cross-sectional areas = (4πd^2) / (πd^2) = 4:1
Since the force applied is the same for both wires, the increase in length is inversely proportional to their cross-sectional areas.
Ratio of increase in length = 1:4 (inverse of 4:1) = 1:4
Therefore, the correct answer is option C) 1:8
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