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Q.

A rod of length L & mass M is having cross section A. The material of rod is having Young’s modules equal to $' Y' .$ If the rod is rotated horizontally about an axis passing through one end and perpendicular to length then ratio of elongation produced in the outer half of the rod to its inner half will be $11 : n,$ find n.

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Detailed Solution

$t e n s i o n = T = \frac{M ω^{2} (L^{2} - x^{2})}{2} Δ L = \int_{0}^{x} \frac{T d x}{y A}$

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A rod of length L & mass M is having cross section A. The material of rod is having Young’s modules equal to 'Y'. If the rod is rotated horizontally about an axis passing through one end and perpendicular to length then ratio of elongation produced in the outer half of the rod to its inner half will be 11:n, find n.