# 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)

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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