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SOHAN SARANGI Grade: 12
        

A uniform rod of mass m and length l rotates in a horizontal plane with an angular velocity w about a vertical axis passing through one end.Find the tension in the rod at a distance x from the axis.

6 years ago

Answers : (4)

SAGAR SINGH - IIT DELHI
879 Points
										

Dear student,


 


Take an element of length dr.


mass per unit length= m/l dr


Tension=integral mw2rdr/L=mw2r2/2L













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6 years ago
SAGAR SINGH - IIT DELHI
879 Points
										

Deat student,


The solution for this has been posted by me. Please do not post the same doubt twice..













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6 years ago
Sai Theja K
19 Points
										

consider a small element dx at a distance x from axis of rod


the centripetol force required is given by tension so,


dT=(dm)(x)(w2


dm=(m/l)dx


integrate it over the limits 0 to X


 

6 years ago
vikas askiitian expert
510 Points
										

let AB is a rod of length l ,mass M & this rod is rotating about end A....


now , mark a point c anywhere on the rod , distance bw end A & C is x ...


now the rod is divided into two parts , AC & CB .......


tension of rod at point C is (T)= dmw2 r                   (dm is mass of part BC = m(l-x)/l )


                                          =M(l-x)w2r/l


this r is the distance of center of mass of BC from end A so r = (x+l)/2


so


           T = M(l-x)(l+x))w2 /2l    


          T = M(l2-x2)w2 /2l 


this is the expression for tension at any point


 

6 years ago
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