Solving a Rotation Mechanics Problem: Option D vs Attempted Solution

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The discussion revolves around a mechanics problem involving a rod and the forces acting at a specific point, labeled as x. The original poster is confused about the correct answer, which is stated to be option (D) in their reference material. They seek clarification on how different parts of the rod contribute to the tension at point x, particularly in relation to their distance from the axis of rotation. After some back-and-forth, the poster confirms that they have resolved their confusion and found the correct answer. The conversation highlights the importance of understanding the distribution of forces in rotational mechanics.
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Hi friends,
Feeling pleasure to share some more aspects with you.
I am getting a doubts in some of the problems.
Thank you all in advance.

The problem is:


Attempt,



But the book says the answer is option (D).
Please friend help to get rid off.
Awaiting for reply.
 
Last edited by a moderator:
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What is the total force felt by the rod at x? Why?
 
voko said:
What is the total force felt by the rod at x? Why?

Sorry voko I don't get it. Please help me in solving.

I am getting the equation for the right side of 'x'.
 
At point x in the rod, there is some force of tension. You computed the force of inertia due to dx just next to x. But what about other parts of the rod? Which parts of the rod contribute to the tension at x: the parts further away from the axis of rotation, or closer to it?
 
voko said:
At point x in the rod, there is some force of tension. You computed the force of inertia due to dx just next to x. But what about other parts of the rod? Which parts of the rod contribute to the tension at x: the parts further away from the axis of rotation, or closer to it?

 
Last edited by a moderator:
Imagine that the rod itself is massless. Now let there be some point mass attached to the rod that is closer to the axis of rotation than x. Will there be any tension at x? Then let there be a point mass further from the point of rotation than x. Will there be any tension at x?
 
voko said:
Imagine that the rod itself is massless. Now let there be some point mass attached to the rod that is closer to the axis of rotation than x. Will there be any tension at x? Then let there be a point mass further from the point of rotation than x. Will there be any tension at x?

Yes outer mass of the rod i.e. the right side part will apply tension on it.

OK let me try it first.
 
Thank you very much friends. I got the answer. Problem has been cleared.
 

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