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Q.

A uniform rod of length l, mass m, cross-sectional area A and Young's modulus Y is rotated in horizontal plane about a fixed vertical axis passing through one end, with a constant angular velocity ω. Find the total extension in the rod due to the tension produced in the rod.

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a

mω2l23AY

b

mω3t33AY

c

mω2l34AY

d

mω3l23AY

answer is A.

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Detailed Solution

Y = T(x)A(∆e∆x); T(x) = ml(l-x)ω2(l-x2+x)⇒ T = mω22l(l2-x2) ; de = mω22AYl(l2-x2)dx⇒ mω22AYl(l3-l33) = mω2l23AYExtension = mω2l23AY
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