Tension in the rod

Classical Mechanics Level 4

A rod of mass \(1 \ \mathrm{kg}\) is hanging vertically as shown, whose linear mass density varies according to the equation \(\lambda(x)=\lambda_o \sin \left(\dfrac{\pi x}{L}\right)\).

Find the tension(in newton) in the rod at \(x=\frac{3L}{4}\).


  • \(g=9.8\frac{m}{s^2}\)
  • \(x\) is measured from the high end to the low end of the rod.

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