Tension in the rod.

IIT JEE Preparation › Mechanics questions › Tension in the rod.

A thin uniform metallic rod of length 0.5 m and radius 0.1 m rotates with an angular velocity 400rad/s in a horizontal plane about a vertical axis passing through one of its ends. Calculate the tension in the rod as a fucntion of distance from axis and the elongation of the rod.
The density of the material of the rod is 10^4 kg/m^3 and the Young's Modulus is 2 x 10^11N/m^2

I used integration and got T=8(pi) *10⁶ * x²
But answer is 8(pi) *10⁶ *[0.25- x²]

Please help with both.

#Physics #Mechanics

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1 Answers

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Euclid ·2010-09-29 18:02:33

the latter part of the rod moves due to the tension(which i think u have missed)

So T = mrÏ‰²

or T = mL (L - x) . (x + L - x2) Ï‰²

T = m2L (L² - x²) Ï‰²

which gives the ans...

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