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A uniform rod of mass m and length l rot...

A uniform rod of mass `m` and length `l` rotates in a horizontal plane with an angular velocity `omega` about a vertical axis passing through one end. The tension in the rod at a distance x from the axis is

A

`(1)/(2)momega^(2)x`

B

`(1)/(2)momega^(2)(1-(x^(2))/(l))`

C

`(1)/(2)momega^(2)l(1-(x^(2))/(l^(2)))`

D

`(1)/(2)momega^(2)l[1-(x)/(l)]`

Text Solution

AI Generated Solution

To find the tension in a uniform rod of mass `m` and length `l` rotating in a horizontal plane with an angular velocity `ω` about a vertical axis passing through one end, we can follow these steps: ### Step-by-Step Solution: 1. **Understanding the System**: - We have a uniform rod of length `l` and mass `m` rotating about a vertical axis at one end with angular velocity `ω`. We need to find the tension in the rod at a distance `x` from the axis of rotation. 2. **Identifying the Element of the Rod**: ...
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Knowledge Check

  • A thin uniform rod of mass m and length L rotates with the constant angular velocity omega about .the vertical axis passing through the rod's suspensjon point O . It describes a carried surface, then:

    A
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  • 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 ?

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  • A thin uniform copper rod length l and mass m rotates unifomly with an angular velocity omega about a vertical axis passing through one of its ends as shown in the figure. Young's modulus of copper is Y. Breaking stress is sigma_(max) , cross sectional area of rod is A and density of rod is uniform. Based on above information, answer the following questions The maximum angular velocity with which the rod can rotate so that is won't break, is

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