question_answer

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? [JEE Main Held on 12-4-2019 Morning]

A)   

B)

C)                 

D)

Correct Answer: D

Solution :

\[T=\int\limits_{x=x}^{x=\ell }{dm{{\omega }^{2}}x}=\int\limits_{x=x}^{x=\ell }{\frac{m}{\ell }}dx{{\omega }^{2}}x\] \[=\frac{m{{\omega }^{2}}}{2\ell }\left( {{\ell }^{2}}-{{x}^{2}} \right)\]\[\]