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A rod AB of length l has a small hook at end A.Initially the rod is held in horizontal position at a height h above a pin S which is vertically below the end A.After the rod is released,the hook at the end A strikes the pin S and the rod swings in a vertical plane about S.For what minimum value of h the rod will rise to a vertical position?
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A rod AB of length l has a small hook at end A.Initially the rod is he...
Answer:
To find the minimum value of h for which the rod rises to a vertical position, we need to consider the conservation of energy.
Initial Energy:
- The rod is held in a horizontal position at a height h above the pin S.
- The potential energy of the rod is mgh.
Final Energy:
- The rod swings in a vertical plane about S.
- At the highest point, the kinetic energy of the rod is zero.
- The potential energy of the rod is now mgl.
Conservation of Energy:
- We can equate the initial potential energy to the final potential energy.
- mgh = mgl
- h = l
Minimum Value of h:
- To find the minimum value of h, we need to consider the fact that the hook at the end of the rod needs to strike the pin S.
- The minimum value of h can be found by equating the potential energy of the rod when the hook strikes the pin to the final potential energy.
- mgh = mgl - mgx
- h = l - x
Therefore, the minimum value of h for which the rod rises to a vertical position is h = l - x.
Community Answer
A rod AB of length l has a small hook at end A.Initially the rod is he...
The answer to this question is
h = l/ 2
When the rod of mass m is at a height of h, it will possess potential energy of mgh and a kinetic energy is zero. After traveling through an angle of 180 degree, it will still process the same value of Total energy.But to come to an vertical position it must travel another 90 degree. The centre of mass of the rod of length L is at its middle at the vertical position.The potential energy of the rod at this vertical position is mgl/2.But to get the minimum value of height we consider that the kinetic energy at this vertical position is zero. Total energy of the system is a constant and therefore
mgh = mgl/2
h = l/2
h = l/ 2
When the rod of mass m is at a height of h, it will possess potential energy of mgh and a kinetic energy is zero. After traveling through an angle of 180 degree, it will still process the same value of Total energy.But to come to an vertical position it must travel another 90 degree. The centre of mass of the rod of length L is at its middle at the vertical position.The potential energy of the rod at this vertical position is mgl/2.But to get the minimum value of height we consider that the kinetic energy at this vertical position is zero. Total energy of the system is a constant and therefore
mgh = mgl/2
h = l/2
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A rod AB of length l has a small hook at end A.Initially the rod is held in horizontal position at a height h above a pin S which is vertically below the end A.After the rod is released,the hook at the end A strikes the pin S and the rod swings in a vertical plane about S.For what minimum value of h the rod will rise to a vertical position?
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A rod AB of length l has a small hook at end A.Initially the rod is held in horizontal position at a height h above a pin S which is vertically below the end A.After the rod is released,the hook at the end A strikes the pin S and the rod swings in a vertical plane about S.For what minimum value of h the rod will rise to a vertical position? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A rod AB of length l has a small hook at end A.Initially the rod is held in horizontal position at a height h above a pin S which is vertically below the end A.After the rod is released,the hook at the end A strikes the pin S and the rod swings in a vertical plane about S.For what minimum value of h the rod will rise to a vertical position? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A rod AB of length l has a small hook at end A.Initially the rod is held in horizontal position at a height h above a pin S which is vertically below the end A.After the rod is released,the hook at the end A strikes the pin S and the rod swings in a vertical plane about S.For what minimum value of h the rod will rise to a vertical position?.
A rod AB of length l has a small hook at end A.Initially the rod is held in horizontal position at a height h above a pin S which is vertically below the end A.After the rod is released,the hook at the end A strikes the pin S and the rod swings in a vertical plane about S.For what minimum value of h the rod will rise to a vertical position? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A rod AB of length l has a small hook at end A.Initially the rod is held in horizontal position at a height h above a pin S which is vertically below the end A.After the rod is released,the hook at the end A strikes the pin S and the rod swings in a vertical plane about S.For what minimum value of h the rod will rise to a vertical position? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A rod AB of length l has a small hook at end A.Initially the rod is held in horizontal position at a height h above a pin S which is vertically below the end A.After the rod is released,the hook at the end A strikes the pin S and the rod swings in a vertical plane about S.For what minimum value of h the rod will rise to a vertical position?.
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