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An iron rod is 2.58m long at 0 degree Celsius. Calculate the length of a brass rod at 0 degree Celsius if the difference between the lengths of the two rods must remain the same at all temperatures (linear expansivity of iron is 1.2*10^-5 and linear expansivity of brass is 1.9*10^-5)?
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An iron rod is 2.58m long at 0 degree Celsius. Calculate the length of...
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An iron rod is 2.58m long at 0 degree Celsius. Calculate the length of...
Problem Statement:
An iron rod is 2.58m long at 0 degree Celsius. Calculate the length of a brass rod at 0 degree Celsius if the difference between the lengths of the two rods must remain the same at all temperatures (linear expansivity of iron is 1.2*10^-5 and linear expansivity of brass is 1.9*10^-5)?
Solution:
Let's assume the length of the brass rod at 0 degree Celsius is Lb.
Step 1: Finding the original difference in length
As per the problem statement, the difference in length between the iron and brass rods must remain the same at all temperatures. Therefore, we can find the original difference in length between the two rods at 0 degree Celsius:
Difference in length = Length of iron rod - Length of brass rod
Difference in length = 2.58m - Lb
Step 2: Finding the new length of the iron rod at a given temperature
Let's assume the new length of the iron rod at a given temperature t is Li(t). We can find Li(t) using the formula:
Li(t) = Li(0) + αiLi(0)(t - 0)
where Li(0) is the original length of the iron rod at 0 degree Celsius, αi is the linear expansivity of iron, and (t - 0) is the change in temperature.
Substituting the given values, we get:
Li(t) = 2.58m + (1.2*10^-5 m/°C) * 2.58m * t
Step 3: Finding the new length of the brass rod at a given temperature
Let's assume the new length of the brass rod at a given temperature t is Lb(t). We can find Lb(t) using the same formula:
Lb(t) = Lb(0) + αbLb(0)(t - 0)
where Lb(0) is the original length of the brass rod at 0 degree Celsius, αb is the linear expansivity of brass, and (t - 0) is the change in temperature.
Substituting the given values, we get:
Lb(t) = Lb + (1.9*10^-5 m/°C) * Lb * t
Step 4: Solving for the new length of the brass rod at 0 degree Celsius
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An iron rod is 2.58m long at 0 degree Celsius. Calculate the length of a brass rod at 0 degree Celsius if the difference between the lengths of the two rods must remain the same at all temperatures (linear expansivity of iron is 1.2*10^-5 and linear expansivity of brass is 1.9*10^-5)?
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An iron rod is 2.58m long at 0 degree Celsius. Calculate the length of a brass rod at 0 degree Celsius if the difference between the lengths of the two rods must remain the same at all temperatures (linear expansivity of iron is 1.2*10^-5 and linear expansivity of brass is 1.9*10^-5)? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about An iron rod is 2.58m long at 0 degree Celsius. Calculate the length of a brass rod at 0 degree Celsius if the difference between the lengths of the two rods must remain the same at all temperatures (linear expansivity of iron is 1.2*10^-5 and linear expansivity of brass is 1.9*10^-5)? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An iron rod is 2.58m long at 0 degree Celsius. Calculate the length of a brass rod at 0 degree Celsius if the difference between the lengths of the two rods must remain the same at all temperatures (linear expansivity of iron is 1.2*10^-5 and linear expansivity of brass is 1.9*10^-5)?.
An iron rod is 2.58m long at 0 degree Celsius. Calculate the length of a brass rod at 0 degree Celsius if the difference between the lengths of the two rods must remain the same at all temperatures (linear expansivity of iron is 1.2*10^-5 and linear expansivity of brass is 1.9*10^-5)? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about An iron rod is 2.58m long at 0 degree Celsius. Calculate the length of a brass rod at 0 degree Celsius if the difference between the lengths of the two rods must remain the same at all temperatures (linear expansivity of iron is 1.2*10^-5 and linear expansivity of brass is 1.9*10^-5)? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An iron rod is 2.58m long at 0 degree Celsius. Calculate the length of a brass rod at 0 degree Celsius if the difference between the lengths of the two rods must remain the same at all temperatures (linear expansivity of iron is 1.2*10^-5 and linear expansivity of brass is 1.9*10^-5)?.
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