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A free bar of length / is uniformly heated from 0°C to a temperature t°C, α is the coefficient of linear expansion and E is the modulus of elasticity. The stress in the bar is
- a)α t E
- b)α t E/2
- c)zero
- d)None of these
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A free bar of length / is uniformly heated from 0°C to a temperatu...
Since the bar is free to expand, no stresses will be developed in the bar.
Most Upvoted Answer
A free bar of length / is uniformly heated from 0°C to a temperatu...
To L. The temperature T(x) at distance x from the left end of the bar is given by the equation T(x) = 100 - 4x, where x is measured in meters. Find the average temperature of the bar over its entire length.
To find the average temperature of the bar over its entire length, we need to find the average value of T(x) over the interval [0, L].
The average value of a function f(x) over an interval [a, b] is given by the formula:
Average value = (1 / (b - a)) * ∫[a to b] f(x) dx
In this case, the interval is [0, L] and the function is T(x) = 100 - 4x. So, the average temperature is:
Average temperature = (1 / L) * ∫[0 to L] (100 - 4x) dx
Integrating, we get:
Average temperature = (1 / L) * [100x - 2x^2] evaluated from 0 to L
Evaluating the integral, we get:
Average temperature = (1 / L) * (100L - 2L^2 - (0 - 0))
Simplifying, we get:
Average temperature = (100L - 2L^2) / L
The L cancels out, leaving us with:
Average temperature = 100 - 2L
Therefore, the average temperature of the bar over its entire length is 100 - 2L.
To find the average temperature of the bar over its entire length, we need to find the average value of T(x) over the interval [0, L].
The average value of a function f(x) over an interval [a, b] is given by the formula:
Average value = (1 / (b - a)) * ∫[a to b] f(x) dx
In this case, the interval is [0, L] and the function is T(x) = 100 - 4x. So, the average temperature is:
Average temperature = (1 / L) * ∫[0 to L] (100 - 4x) dx
Integrating, we get:
Average temperature = (1 / L) * [100x - 2x^2] evaluated from 0 to L
Evaluating the integral, we get:
Average temperature = (1 / L) * (100L - 2L^2 - (0 - 0))
Simplifying, we get:
Average temperature = (100L - 2L^2) / L
The L cancels out, leaving us with:
Average temperature = 100 - 2L
Therefore, the average temperature of the bar over its entire length is 100 - 2L.
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