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Two uniform rods A and B of length 0.6 m each and of masses 0.01 kg and 0.02 kg respectively are rigidly joined end to end. The combination is pivoted at the lighter end, P as shown in figure. Such that it can freely rotate about point P in a vertical plane. A small object of mass 0.05 kg, moving horizontally, hits the lower end of the combination and sticks to it. What should be the velocity of the object, so that the system could just be raised to the horizontal position?
Most Upvoted Answer
Two uniform rods A and B of length 0.6 m each and of masses 0.01 kg an...
Since ,fig is not given so, I am not able to visualise the situation whether the system is vertically straight or form angular shape.
But I can give u hint to solve it.
Just do one thing
(1) apply angular momentum conservation about point P
(2) total mechanical conservation
note: momentum is not conserved because point P will exertnal force.
omega will be same, calculate moi very carefully.
But I can give u hint to solve it.
Just do one thing
(1) apply angular momentum conservation about point P
(2) total mechanical conservation
note: momentum is not conserved because point P will exertnal force.
omega will be same, calculate moi very carefully.
Community Answer
Two uniform rods A and B of length 0.6 m each and of masses 0.01 kg an...
Solution:
Understanding the problem
- Two uniform rods A and B of length 0.6 m each and of masses 0.01 kg and 0.02 kg respectively are rigidly joined end to end.
- The combination is pivoted at the lighter end, P as shown in figure. Such that it can freely rotate about point P in a vertical plane.
- A small object of mass 0.05 kg, moving horizontally, hits the lower end of the combination and sticks to it.
- We need to find the velocity of the object, so that the system could just be raised to the horizontal position.
Solution
- Let the velocity of the object be v.
- The initial momentum of the object = m * v, where m is the mass of the object.
- When the object sticks to the system, the system acquires a linear velocity and an angular velocity.
- Let the linear velocity of the system be V and the angular velocity be ω.
- Then, using the principle of conservation of linear momentum, we have:
- (m + M)V = m * v
- where M is the total mass of the system and is equal to mA + mB + m, where mA and mB are the masses of rods A and B respectively.
- Using the principle of conservation of angular momentum, we have:
- Iω = mv * r, where I is the moment of inertia of the system about the pivot point P and r is the distance between the pivot point P and the centre of mass of the system.
- The moment of inertia of the system about the pivot point P can be calculated as:
- I = IA + IB + IC
- where IA and IB are the moments of inertia of rods A and B respectively about their respective centres and IC is the moment of inertia of the combination about the centre of mass of the system.
- The distance between the pivot point P and the centre of mass of the system can be calculated as:
- r = (mA * lA + mB * lB + m * l) / M
- where lA and lB are the distances of the centres of rods A and B respectively from the pivot point P and l is the distance of the object from
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Two uniform rods A and B of length 0.6 m each and of masses 0.01 kg and 0.02 kg respectively are rigidly joined end to end. The combination is pivoted at the lighter end, P as shown in figure. Such that it can freely rotate about point P in a vertical plane. A small object of mass 0.05 kg, moving horizontally, hits the lower end of the combination and sticks to it. What should be the velocity of the object, so that the system could just be raised to the horizontal position?
Question Description
Two uniform rods A and B of length 0.6 m each and of masses 0.01 kg and 0.02 kg respectively are rigidly joined end to end. The combination is pivoted at the lighter end, P as shown in figure. Such that it can freely rotate about point P in a vertical plane. A small object of mass 0.05 kg, moving horizontally, hits the lower end of the combination and sticks to it. What should be the velocity of the object, so that the system could just be raised to the horizontal position? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Two uniform rods A and B of length 0.6 m each and of masses 0.01 kg and 0.02 kg respectively are rigidly joined end to end. The combination is pivoted at the lighter end, P as shown in figure. Such that it can freely rotate about point P in a vertical plane. A small object of mass 0.05 kg, moving horizontally, hits the lower end of the combination and sticks to it. What should be the velocity of the object, so that the system could just be raised to the horizontal position? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two uniform rods A and B of length 0.6 m each and of masses 0.01 kg and 0.02 kg respectively are rigidly joined end to end. The combination is pivoted at the lighter end, P as shown in figure. Such that it can freely rotate about point P in a vertical plane. A small object of mass 0.05 kg, moving horizontally, hits the lower end of the combination and sticks to it. What should be the velocity of the object, so that the system could just be raised to the horizontal position?.
Two uniform rods A and B of length 0.6 m each and of masses 0.01 kg and 0.02 kg respectively are rigidly joined end to end. The combination is pivoted at the lighter end, P as shown in figure. Such that it can freely rotate about point P in a vertical plane. A small object of mass 0.05 kg, moving horizontally, hits the lower end of the combination and sticks to it. What should be the velocity of the object, so that the system could just be raised to the horizontal position? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Two uniform rods A and B of length 0.6 m each and of masses 0.01 kg and 0.02 kg respectively are rigidly joined end to end. The combination is pivoted at the lighter end, P as shown in figure. Such that it can freely rotate about point P in a vertical plane. A small object of mass 0.05 kg, moving horizontally, hits the lower end of the combination and sticks to it. What should be the velocity of the object, so that the system could just be raised to the horizontal position? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two uniform rods A and B of length 0.6 m each and of masses 0.01 kg and 0.02 kg respectively are rigidly joined end to end. The combination is pivoted at the lighter end, P as shown in figure. Such that it can freely rotate about point P in a vertical plane. A small object of mass 0.05 kg, moving horizontally, hits the lower end of the combination and sticks to it. What should be the velocity of the object, so that the system could just be raised to the horizontal position?.
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Two uniform rods A and B of length 0.6 m each and of masses 0.01 kg and 0.02 kg respectively are rigidly joined end to end. The combination is pivoted at the lighter end, P as shown in figure. Such that it can freely rotate about point P in a vertical plane. A small object of mass 0.05 kg, moving horizontally, hits the lower end of the combination and sticks to it. What should be the velocity of the object, so that the system could just be raised to the horizontal position?, a detailed solution for Two uniform rods A and B of length 0.6 m each and of masses 0.01 kg and 0.02 kg respectively are rigidly joined end to end. The combination is pivoted at the lighter end, P as shown in figure. Such that it can freely rotate about point P in a vertical plane. A small object of mass 0.05 kg, moving horizontally, hits the lower end of the combination and sticks to it. What should be the velocity of the object, so that the system could just be raised to the horizontal position? has been provided alongside types of Two uniform rods A and B of length 0.6 m each and of masses 0.01 kg and 0.02 kg respectively are rigidly joined end to end. The combination is pivoted at the lighter end, P as shown in figure. Such that it can freely rotate about point P in a vertical plane. A small object of mass 0.05 kg, moving horizontally, hits the lower end of the combination and sticks to it. What should be the velocity of the object, so that the system could just be raised to the horizontal position? theory, EduRev gives you an
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