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I have a doubt, kindly clarify. A uniform rod of length l is being rotated in a horizontal plane with a constant angular speed about an axis passing through one of its ends. If the tension generated in the rod due to rotation is T(x) at a distance x f

A uniform rod of length l is being rotated in a horizontal plane with a constant angular speed about an axis passing through one of its ends. If the tension generated in the rod due to rotation is T(x) at a distance x from the axis, then which of the following graphs depicts it most closely ?

  • Option 1)

  • Option 2)

  • Option 3)

  • Option 4)

Answers (1)
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Centripetal Force -

F=4m\pi^{2}n^{2}r

F=\frac {4m\pi^{2}n^{2}r} {T^{2}}

F = Centripetal force

\omega= Angular velocity

n = frequency

- wherein

Force acts on the body along the radius and towards centre.

 

 

T=dm w^{2}r                             

                                         \left [ dm=\frac{m}{l}(l-x) \right ]

                                          r=x+\frac{l-x}{2}

\Rightarrow T=\frac{m}{l}(l-x)w^{2}\cdot \left ( x+\frac{l-x}{2} \right )

\Rightarrow T=\frac{mw^{2}}{2l}(l^{2}-x^{2})..............This equation follows graph(1)

 


Option 1)

Option 2)

Option 3)

Option 4)

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