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Two identical blocks A and B each of mass 'm' resting on smooth floor are connected by a light spring of natural length L and spring constant K, with the spring at its natural length. A third identical block C moving with a speed ν along the line joining A and B collides with A. the maximum compression in the spring is
- a)ν√m∕2k
- b)m√ν∕2k
- c)√mν∕k
- d)mν/2k
Correct answer is option 'A'. Can you explain this answer?
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Two identical blocks A and B each of mass 'm' resting on smoot...
Let's assume that block C collides with block A, causing them to stick together. We can then analyze the motion of the combined block AC as they move away from block B.
Before the collision, block C has a kinetic energy of 1/2 mv^2. This kinetic energy is transferred to the spring-block system during the collision. The spring is compressed by a distance x, so the potential energy stored in the spring is 1/2 kx^2.
Since the spring-block system starts from rest, the total energy of the system is equal to the potential energy stored in the spring. Therefore, we have:
1/2 mv^2 = 1/2 kx^2
Solving for x, we get:
x = sqrt(mv^2/k)
This is the maximum compression of the spring when block C collides with block A.
Now, let's analyze the motion of the combined block AC as they move away from block B. Since block B is at rest, the center of mass of the system moves at a constant velocity. However, the spring between blocks A and C is compressed, which will cause them to oscillate around the center of mass.
The period of oscillation can be found using the formula:
T = 2*pi*sqrt(meff/k)
where meff is the effective mass of the system, given by:
1/meff = 1/m + 1/m
Substituting the values, we get:
T = 2*pi*sqrt(2m/k)
Therefore, the period of oscillation depends only on the mass of the blocks and the spring constant, and is independent of the initial velocity of block C.
In summary, when block C collides with block A, they stick together and oscillate around the center of mass of the system with a period given by T = 2*pi*sqrt(2m/k). Block B remains at rest throughout the motion.
Before the collision, block C has a kinetic energy of 1/2 mv^2. This kinetic energy is transferred to the spring-block system during the collision. The spring is compressed by a distance x, so the potential energy stored in the spring is 1/2 kx^2.
Since the spring-block system starts from rest, the total energy of the system is equal to the potential energy stored in the spring. Therefore, we have:
1/2 mv^2 = 1/2 kx^2
Solving for x, we get:
x = sqrt(mv^2/k)
This is the maximum compression of the spring when block C collides with block A.
Now, let's analyze the motion of the combined block AC as they move away from block B. Since block B is at rest, the center of mass of the system moves at a constant velocity. However, the spring between blocks A and C is compressed, which will cause them to oscillate around the center of mass.
The period of oscillation can be found using the formula:
T = 2*pi*sqrt(meff/k)
where meff is the effective mass of the system, given by:
1/meff = 1/m + 1/m
Substituting the values, we get:
T = 2*pi*sqrt(2m/k)
Therefore, the period of oscillation depends only on the mass of the blocks and the spring constant, and is independent of the initial velocity of block C.
In summary, when block C collides with block A, they stick together and oscillate around the center of mass of the system with a period given by T = 2*pi*sqrt(2m/k). Block B remains at rest throughout the motion.
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Two identical blocks A and B each of mass 'm' resting on smooth floor are connected by a light spring of natural length L and spring constant K, with the spring at its natural length. A third identical block C moving with a speed ν along the line joining A and B collides with A. the maximum compression in the spring isa)ν√m∕2kb)m√ν∕2kc)√mν∕kd)mν/2kCorrect answer is option 'A'. Can you explain this answer?
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Two identical blocks A and B each of mass 'm' resting on smooth floor are connected by a light spring of natural length L and spring constant K, with the spring at its natural length. A third identical block C moving with a speed ν along the line joining A and B collides with A. the maximum compression in the spring isa)ν√m∕2kb)m√ν∕2kc)√mν∕kd)mν/2kCorrect answer is option 'A'. 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 identical blocks A and B each of mass 'm' resting on smooth floor are connected by a light spring of natural length L and spring constant K, with the spring at its natural length. A third identical block C moving with a speed ν along the line joining A and B collides with A. the maximum compression in the spring isa)ν√m∕2kb)m√ν∕2kc)√mν∕kd)mν/2kCorrect answer is option 'A'. 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 identical blocks A and B each of mass 'm' resting on smooth floor are connected by a light spring of natural length L and spring constant K, with the spring at its natural length. A third identical block C moving with a speed ν along the line joining A and B collides with A. the maximum compression in the spring isa)ν√m∕2kb)m√ν∕2kc)√mν∕kd)mν/2kCorrect answer is option 'A'. Can you explain this answer?.
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