Verified Solution • 2025–26 Session moderate

QJEEM19Ph4933: JEE Main 2019 Physics - Class 11 JEEM19Ph4933 Solution: A uniform rod of length is being rotated in a horizontal plane…

A uniform rod of length ℓ\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?

Multiple Choice Options

  • A https://ik.imagekit.io/novatra/photos/2021c0603738f18ffb0d7b527f46f3160abf729c33099eb4dc2a0790cb8da910.webp
  • B https://ik.imagekit.io/novatra/photos/3a5636a54ff92febdbe2750f546f8f2573d912464871363b7b1601adeab4be2d.webp
  • C https://ik.imagekit.io/novatra/photos/82f9c9e370191723a3f75b047237ae993a809c38120096b0c4ae851153c5d8ee.webp
  • D https://ik.imagekit.io/novatra/photos/2c4f10c9d5c92409770d4d44bd6d10700c5c4244ca3d46695f1689cbb4a1146f.webp

Step-by-Step Verified Solution

T=∫x=xx=ℓdmω2x=∫x=xx=ℓmℓdxω2x TT = \int\limits_{x = x}^{x = \ell } {dm{\omega ^2}} x = \int\limits_{x = x}^{x = \ell } {{m \over \ell }} dx{\omega ^2}x\,T

=mω22ℓ(ℓ2−x2)= {{m{\omega ^2}} \over {2\ell }}\left( {{\ell ^2} - {x^2}} \right)

∴T=mω22ℓ(ℓ2−x2)\therefore T = {{m{\omega ^2}} \over {2\ell }}\left( {{\ell ^2} - {x^2}} \right)

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