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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?

Solution:

Correct option is D.

T = ∫xℓ dm ω²x = ∫xℓ (mℓ)dx ω²x = mω²2ℓ(ℓ² - x²)
T = mω²2ℓ(ℓ² - x²)