A uniform rod of mass m and length l rotates in a horizontal plane with an angular velocity ω about a vertical axis passing through one end. The tension in the rod at a distance x from the axis is
A
12mω2x
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B
12mω2x2l
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C
12mω2l(1−x1)
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D
12.mω2l[l2−x2]
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Solution
The correct option is C12.mω2l[l2−x2] The mass of the element =dm=mldx The force on the element towards the axis =T−(T+dT)=−dT ∴−dT=(dm)ω2x=(mldx)ω2x T=−mω2l.x22+constant For x=1,T=0. ∴theconstant=12.mω2l2l ∴T=12.mω2l(l2−x2)