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Grade: 11
        
A uniform rod of mass m and length l rotates in a horizontal plane with an angular velocity w about a vertical axis passsing through one end.The tension in the rod at a distance x from the axis is 
one year ago

Answers : (1)

Khimraj
3008 Points
							

Considering a small portion of dr in the rod at a distance r from the axis of the rod.

So,mass of this portion will be dm=mldr (as uniform rod is mentioned)

Now,tension on that part will be the Centrifugal force acting on it, i.e dT=dmω2r (because,tension is directed away from the centre whereas,r is being counted towards the centre,if you solve it considering Centripetal force,then the force will be positive but limit will be counted from r to l)

Or, dT=mldrω2r

So, T0dT=mlω2xlrdr (as,at r=l,T=0)

So, T=mω22l(x2l2)=mω22l(l2x2)

one year ago
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