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# 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.

10 years ago

Dear student,

Take an element of length dr.

mass per unit length= m/l dr

Tension=integral mw2rdr/L=mw2r2/2L

All the best.

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Sagar Singh

B.Tech, IIT Delhi

sagarsingh24.iitd@gmail.com 10 years ago

Deat student,

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

All the best.

Win exciting gifts by answering the questions on Discussion Forum. So help discuss any query on askiitians forum and become an Elite Expert League askiitian.

Sagar Singh

B.Tech, IIT Delhi

sagarsingh24.iitd@gmail.com

10 years ago

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

10 years ago

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

3 years ago
For length l mass is is m therefor For dx length mass will be m/ldx Now force observed by this element will be m/l xdx w2 Now integrate with limit 0,to l to get the answer Kushagra Madhukar
one year ago
Dear student,

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       (Integrating)
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

Hope this helps.
Thanks and regards,
Kushagra