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Question

A uniform rod of mass 'm' and length 'L' is tied to a vertical shaft. It rotates in horizontal plane about the vertical axis at angular velocity ω. How much horizontal force does the shaft excert on the rod?

A
mw2L
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B
Mw2L2
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C
mw2L4
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D
zero
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Solution

The correct option is B Mw2L2
Let T be the force applied horizontally on the rod. The acceleration of centre of mass is ω2L2, as it is moving in a circle of radius L2 .
Using Fext=MacmT=Mω2(L2)
Thus, the horizontal force exerted is 12Mω2L

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