Grade 12Mechanics

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.

SOHAN SARANGI

15 Years agoGrade 12

6 Answers

SAGAR SINGH - IIT DELHI

15 Years ago

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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Sagar Singh

B.Tech, IIT Delhi

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SAGAR SINGH - IIT DELHI

15 Years ago

Deat student,

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

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Sagar Singh

B.Tech, IIT Delhi

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Sai Theja K

15 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

vikas askiitian expert

15 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

T = M(l-x)(l+x))w² /2l

T = M(l²-x²)w² /2l

this is the expression for tension at any point

Aryan

8 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

6 Years ago

Dear student,

Please find the attached solution to your problem below.

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

T = M(l-x)(l+x))w² /2l

T = M(l²-x²)w² /2l

Hope this helps.

Thanks and regards,

Kushagra