JEE MAIN - Physics (2019 - 12th April Morning Slot - No. 20)
A uniform rod of length $$\ell $$ 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?
_12th_April_Morning_Slot_en_20_1.png)
_12th_April_Morning_Slot_en_20_2.png)
_12th_April_Morning_Slot_en_20_3.png)
_12th_April_Morning_Slot_en_20_4.png)
Explanation
$$T = \int\limits_{x = x}^{x = \ell } {dm{\omega ^2}} x = \int\limits_{x = x}^{x = \ell } {{m \over \ell }} dx{\omega ^2}x\,T$$
$$ = {{m{\omega ^2}} \over {2\ell }}\left( {{\ell ^2} - {x^2}} \right)$$
$$ \therefore T = {{m{\omega ^2}} \over {2\ell }}\left( {{\ell ^2} - {x^2}} \right)$$
$$ = {{m{\omega ^2}} \over {2\ell }}\left( {{\ell ^2} - {x^2}} \right)$$
$$ \therefore T = {{m{\omega ^2}} \over {2\ell }}\left( {{\ell ^2} - {x^2}} \right)$$
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