A uniform rod of length l is being rotated in a horizontal plane with a constant angular speed about

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3-2.Motion in Plane

hard

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?

(JEE MAIN-2019)

Solution

$T = \int_{x – x}^{x – \ell } {dm{\omega ^2}x = \int_{x – x}^{x – \ell } {\frac{m}{\ell }dx{\omega ^2}x\,T} } $
$ = \frac{{m{\omega ^2}}}{{2\ell }}\left( {{\ell ^2} – {x^2}} \right)$
$T = \frac{{m{\omega ^2}}}{{2\ell }}\left( {{\ell ^2} – {x^2}} \right)$

Standard 11

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Solution

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