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A thin uniform metallic rod of length 0.5 m and radius 0.1 m with an angular velocity 400 rad s-1 in a horizontal plane about a vertical axis passing through one of its ends. Elongation in the rod is (in m) [Given density of material of the rod is 104kgm-3 and Y=2×1011Nm-2 ]

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a

10-33

b

310-3

c

2102

d

1022

answer is A.

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Detailed Solution

Consider an element of length dx at a distance x from the axis of rotation,dF=dmxω2 =ρAdx·x·ω2 F=ρAω2∫xLxdx =12ρAω2L2-x2 If dy is the elongation in the element of length dx, thendydx=FAY dy=FdxA·YΔl=ρω22Y∫0LL2-x2dx Δl=ρω2·L23Y Δl=104×(400)2×1232×1011=10-33 m

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A thin uniform metallic rod of length 0.5 m and radius 0.1 m with an angular velocity 400 rad s-1 in a horizontal plane about a vertical axis passing through one of its ends. Elongation in the rod is (in m) [Given density of material of the rod is 104kgm-3 and Y=2×1011Nm-2 ]