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Consider the following two statements : A Linear momentum of a system of particles is zero B. Kinetic energy of a system of particles is zero.Then
- a)A does not imply B and B does not imply A
- b)A implies B but B does not imply A
- c)A does not imply B but B implies A
- d)A implies B and B implies A
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Consider the following two statements :A Linear momentum of a system o...
Kinetic energy of a system of particle is zero only when the speed of each particles is zero. And if speed of each particle is zero, the linear momentum of the system of particle has to be zero.
Also the linear momentum of the system may be zero even when the particles are moving. This is because linear momentum is a vector quantity. In this case the kinetic energy of the system of particles will not be zero.
Also the linear momentum of the system may be zero even when the particles are moving. This is because linear momentum is a vector quantity. In this case the kinetic energy of the system of particles will not be zero.
∴ A does not imply B but B implies A.
Most Upvoted Answer
Consider the following two statements :A Linear momentum of a system o...
The correct answer is option 'C': A does not imply B but B implies A.
Explanation:
To understand why option 'C' is the correct answer, let's analyze each statement individually.
Statement A: "Linear momentum of a system of particles is zero"
Linear momentum is defined as the product of mass and velocity. If the linear momentum of a system of particles is zero, it means that the total mass of the system is zero or the total velocity of the system is zero or both.
Statement B: "Kinetic energy of a system of particles is zero"
Kinetic energy is defined as the energy possessed by an object due to its motion. If the kinetic energy of a system of particles is zero, it means that the total energy of motion of all the particles in the system is zero.
Now let's analyze the relationship between these two statements.
1. A does not imply B:
If the linear momentum of a system of particles is zero, it does not necessarily mean that the kinetic energy of the system is zero. The kinetic energy depends not only on the motion but also on the masses of the particles. Even if the velocity is zero, the masses can still contribute to the kinetic energy.
2. B does not imply A:
If the kinetic energy of a system of particles is zero, it does not necessarily mean that the linear momentum of the system is zero. The kinetic energy can be zero if the particles are at rest or if they have equal and opposite velocities. However, the linear momentum can still be non-zero if the masses of the particles are not equal or if their velocities are not opposite.
3. B implies A:
If the kinetic energy of a system of particles is zero, it implies that the total velocity of the system is zero. This is because kinetic energy is directly proportional to the square of velocity. If the kinetic energy is zero, the velocity must also be zero.
Therefore, the correct answer is option 'C': A does not imply B but B implies A.
Explanation:
To understand why option 'C' is the correct answer, let's analyze each statement individually.
Statement A: "Linear momentum of a system of particles is zero"
Linear momentum is defined as the product of mass and velocity. If the linear momentum of a system of particles is zero, it means that the total mass of the system is zero or the total velocity of the system is zero or both.
Statement B: "Kinetic energy of a system of particles is zero"
Kinetic energy is defined as the energy possessed by an object due to its motion. If the kinetic energy of a system of particles is zero, it means that the total energy of motion of all the particles in the system is zero.
Now let's analyze the relationship between these two statements.
1. A does not imply B:
If the linear momentum of a system of particles is zero, it does not necessarily mean that the kinetic energy of the system is zero. The kinetic energy depends not only on the motion but also on the masses of the particles. Even if the velocity is zero, the masses can still contribute to the kinetic energy.
2. B does not imply A:
If the kinetic energy of a system of particles is zero, it does not necessarily mean that the linear momentum of the system is zero. The kinetic energy can be zero if the particles are at rest or if they have equal and opposite velocities. However, the linear momentum can still be non-zero if the masses of the particles are not equal or if their velocities are not opposite.
3. B implies A:
If the kinetic energy of a system of particles is zero, it implies that the total velocity of the system is zero. This is because kinetic energy is directly proportional to the square of velocity. If the kinetic energy is zero, the velocity must also be zero.
Therefore, the correct answer is option 'C': A does not imply B but B implies A.
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Consider the following two statements :A Linear momentum of a system of particles is zero B. Kinetic energy of a system of particles is zero.Thena)A does not imply B and B does not imply Ab)A implies B but B does not imply Ac)A does not imply B but B implies Ad)A implies B and B implies ACorrect answer is option 'C'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Consider the following two statements :A Linear momentum of a system of particles is zero B. Kinetic energy of a system of particles is zero.Thena)A does not imply B and B does not imply Ab)A implies B but B does not imply Ac)A does not imply B but B implies Ad)A implies B and B implies ACorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the following two statements :A Linear momentum of a system of particles is zero B. Kinetic energy of a system of particles is zero.Thena)A does not imply B and B does not imply Ab)A implies B but B does not imply Ac)A does not imply B but B implies Ad)A implies B and B implies ACorrect answer is option 'C'. Can you explain this answer?.
Consider the following two statements :A Linear momentum of a system of particles is zero B. Kinetic energy of a system of particles is zero.Thena)A does not imply B and B does not imply Ab)A implies B but B does not imply Ac)A does not imply B but B implies Ad)A implies B and B implies ACorrect answer is option 'C'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Consider the following two statements :A Linear momentum of a system of particles is zero B. Kinetic energy of a system of particles is zero.Thena)A does not imply B and B does not imply Ab)A implies B but B does not imply Ac)A does not imply B but B implies Ad)A implies B and B implies ACorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the following two statements :A Linear momentum of a system of particles is zero B. Kinetic energy of a system of particles is zero.Thena)A does not imply B and B does not imply Ab)A implies B but B does not imply Ac)A does not imply B but B implies Ad)A implies B and B implies ACorrect answer is option 'C'. Can you explain this answer?.
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Consider the following two statements :A Linear momentum of a system of particles is zero B. Kinetic energy of a system of particles is zero.Thena)A does not imply B and B does not imply Ab)A implies B but B does not imply Ac)A does not imply B but B implies Ad)A implies B and B implies ACorrect answer is option 'C'. Can you explain this answer?, a detailed solution for Consider the following two statements :A Linear momentum of a system of particles is zero B. Kinetic energy of a system of particles is zero.Thena)A does not imply B and B does not imply Ab)A implies B but B does not imply Ac)A does not imply B but B implies Ad)A implies B and B implies ACorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of Consider the following two statements :A Linear momentum of a system of particles is zero B. Kinetic energy of a system of particles is zero.Thena)A does not imply B and B does not imply Ab)A implies B but B does not imply Ac)A does not imply B but B implies Ad)A implies B and B implies ACorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Consider the following two statements :A Linear momentum of a system of particles is zero B. Kinetic energy of a system of particles is zero.Thena)A does not imply B and B does not imply Ab)A implies B but B does not imply Ac)A does not imply B but B implies Ad)A implies B and B implies ACorrect answer is option 'C'. Can you explain this answer? tests, examples and also practice JEE tests.
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