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?

Question

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?, , , ,

MARKS App · Accepted Answer

The mass of the rod at a distance x from the axis is d m = M L . d x T = ( d m ) ω 2 x Integrating the above equation from x to L = ∫ x L M L ω 2 x d x = M L ω 2 x 2 2 x L M 2 L ω 2 L 2 - x 2 The above equation depicts the relation between tension and length of rod as downward opening parabola.

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