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Two rigid bodies A and B rotate with rotational kinetic energies EA and EBrespectively. The moments of inertia of A and B about the axis of rotation are IA and IB respectively.
If IA = IB and EA = 100 = EB the ratio of 4 angular momentum (LA) of A to the angular momentum (LB) of B is
- a)25
- b)5/4
- c)5
- d)1/4
Correct answer is option 'C'. Can you explain this answer?
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Two rigid bodies A and B rotate with rotational kinetic energies EAand...
Given:
- Two rigid bodies A and B
- Rotational kinetic energies EA and EB
- Moments of inertia IA and IB
- IA = IB
- EA = 100 = EB
To find:
- The ratio of angular momentum LA of A to the angular momentum LB of B
**Solution:**
**Step 1: Understanding rotational kinetic energy and angular momentum**
- Rotational kinetic energy is the energy possessed by a rotating object due to its motion.
- It is given by the formula: KE = (1/2) Iω^2, where I is the moment of inertia and ω is the angular velocity.
- Angular momentum is a measure of the rotational motion of an object.
- It is given by the formula: L = Iω, where I is the moment of inertia and ω is the angular velocity.
**Step 2: Finding the relationship between rotational kinetic energy and angular momentum**
- We can rewrite the formulas for rotational kinetic energy and angular momentum as:
- KE = (1/2) Iω^2
- L = Iω
- Dividing the equation for angular momentum by the equation for rotational kinetic energy, we get:
- L/KE = (Iω) / ((1/2) Iω^2)
- L/KE = 2/ω
- This shows that the ratio of angular momentum to rotational kinetic energy is equal to 2 divided by the angular velocity.
**Step 3: Comparing the rotational kinetic energies and finding the ratio of angular momenta**
- Given that EA = 100 = EB, we can conclude that the rotational kinetic energies of A and B are equal.
- Since the rotational kinetic energy is the same for both bodies, the angular velocities ωA and ωB must also be the same.
- Therefore, the ratio of angular momenta LA/LB can be found using the equation L/KE = 2/ω:
- LA/EA = LB/EB
- LA/100 = LB/100
- LA = LB
- Therefore, the ratio of angular momentum LA of A to the angular momentum LB of B is 1:1 or 1.
**Step 4: Simplifying the ratio**
- Since the question asks for the ratio in terms of a fraction, we can simplify the ratio LA/LB = 1/1 as:
- LA/LB = 1/1 = 1
- Therefore, the ratio of angular momentum LA of A to the angular momentum LB of B is 1.
**Step 5: Identifying the correct option**
- Option (C) states that the ratio is 5, which is incorrect.
- Therefore, the correct answer is option (D) - 1/4.
- Two rigid bodies A and B
- Rotational kinetic energies EA and EB
- Moments of inertia IA and IB
- IA = IB
- EA = 100 = EB
To find:
- The ratio of angular momentum LA of A to the angular momentum LB of B
**Solution:**
**Step 1: Understanding rotational kinetic energy and angular momentum**
- Rotational kinetic energy is the energy possessed by a rotating object due to its motion.
- It is given by the formula: KE = (1/2) Iω^2, where I is the moment of inertia and ω is the angular velocity.
- Angular momentum is a measure of the rotational motion of an object.
- It is given by the formula: L = Iω, where I is the moment of inertia and ω is the angular velocity.
**Step 2: Finding the relationship between rotational kinetic energy and angular momentum**
- We can rewrite the formulas for rotational kinetic energy and angular momentum as:
- KE = (1/2) Iω^2
- L = Iω
- Dividing the equation for angular momentum by the equation for rotational kinetic energy, we get:
- L/KE = (Iω) / ((1/2) Iω^2)
- L/KE = 2/ω
- This shows that the ratio of angular momentum to rotational kinetic energy is equal to 2 divided by the angular velocity.
**Step 3: Comparing the rotational kinetic energies and finding the ratio of angular momenta**
- Given that EA = 100 = EB, we can conclude that the rotational kinetic energies of A and B are equal.
- Since the rotational kinetic energy is the same for both bodies, the angular velocities ωA and ωB must also be the same.
- Therefore, the ratio of angular momenta LA/LB can be found using the equation L/KE = 2/ω:
- LA/EA = LB/EB
- LA/100 = LB/100
- LA = LB
- Therefore, the ratio of angular momentum LA of A to the angular momentum LB of B is 1:1 or 1.
**Step 4: Simplifying the ratio**
- Since the question asks for the ratio in terms of a fraction, we can simplify the ratio LA/LB = 1/1 as:
- LA/LB = 1/1 = 1
- Therefore, the ratio of angular momentum LA of A to the angular momentum LB of B is 1.
**Step 5: Identifying the correct option**
- Option (C) states that the ratio is 5, which is incorrect.
- Therefore, the correct answer is option (D) - 1/4.
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Two rigid bodies A and B rotate with rotational kinetic energies EAand EBrespectively. The moments of inertia of A and B about the axis of rotation are IAand IBrespectively.If IA= IBand EA= 100 = EBthe ratio of 4 angular momentum (LA) of A to the angular momentum (LB) of B isa)25b)5/4c)5d)1/4Correct answer is option 'C'. Can you explain this answer?
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Two rigid bodies A and B rotate with rotational kinetic energies EAand EBrespectively. The moments of inertia of A and B about the axis of rotation are IAand IBrespectively.If IA= IBand EA= 100 = EBthe ratio of 4 angular momentum (LA) of A to the angular momentum (LB) of B isa)25b)5/4c)5d)1/4Correct answer is option 'C'. Can you explain this answer? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Two rigid bodies A and B rotate with rotational kinetic energies EAand EBrespectively. The moments of inertia of A and B about the axis of rotation are IAand IBrespectively.If IA= IBand EA= 100 = EBthe ratio of 4 angular momentum (LA) of A to the angular momentum (LB) of B isa)25b)5/4c)5d)1/4Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two rigid bodies A and B rotate with rotational kinetic energies EAand EBrespectively. The moments of inertia of A and B about the axis of rotation are IAand IBrespectively.If IA= IBand EA= 100 = EBthe ratio of 4 angular momentum (LA) of A to the angular momentum (LB) of B isa)25b)5/4c)5d)1/4Correct answer is option 'C'. Can you explain this answer?.
Two rigid bodies A and B rotate with rotational kinetic energies EAand EBrespectively. The moments of inertia of A and B about the axis of rotation are IAand IBrespectively.If IA= IBand EA= 100 = EBthe ratio of 4 angular momentum (LA) of A to the angular momentum (LB) of B isa)25b)5/4c)5d)1/4Correct answer is option 'C'. Can you explain this answer? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Two rigid bodies A and B rotate with rotational kinetic energies EAand EBrespectively. The moments of inertia of A and B about the axis of rotation are IAand IBrespectively.If IA= IBand EA= 100 = EBthe ratio of 4 angular momentum (LA) of A to the angular momentum (LB) of B isa)25b)5/4c)5d)1/4Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two rigid bodies A and B rotate with rotational kinetic energies EAand EBrespectively. The moments of inertia of A and B about the axis of rotation are IAand IBrespectively.If IA= IBand EA= 100 = EBthe ratio of 4 angular momentum (LA) of A to the angular momentum (LB) of B isa)25b)5/4c)5d)1/4Correct answer is option 'C'. Can you explain this answer?.
Solutions for Two rigid bodies A and B rotate with rotational kinetic energies EAand EBrespectively. The moments of inertia of A and B about the axis of rotation are IAand IBrespectively.If IA= IBand EA= 100 = EBthe ratio of 4 angular momentum (LA) of A to the angular momentum (LB) of B isa)25b)5/4c)5d)1/4Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for NEET.
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