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A particle performs uniform circular motion with an angular momentum L. If the frequency of particle's motion is doubled and its kinetic energy is halved, the angular momentum becomes
- a)2L
- b)4L
- c)L/2
- d)L/4
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
A particle performs uniform circular motion with an angular momentum L...
Explanation:
Angular momentum (L) of a particle performing uniform circular motion is given as:
L = mvR
where m is the mass of the particle, v is its velocity, and R is the radius of the circular path.
When the frequency of particle's motion is doubled, the velocity of the particle also doubles since v = 2πfR. Therefore, the new angular momentum (L') is given as:
L' = m(2v)R = 2mvR = 2L
When the kinetic energy of the particle is halved, its velocity becomes √(1/2) times its original value since KE = (1/2)mv^2. Therefore, the new angular momentum (L'') is given as:
L'' = m(√(1/2)v)R = (1/√2)mvR = (1/√2)L
Therefore, the ratio of the new angular momentum to the original angular momentum is:
L''/L = (1/√2)L/L = L/√2L = (1/√2)
Simplifying, we get:
L'' = (1/√2)L = L/2
Hence, option D is the correct answer.
Angular momentum (L) of a particle performing uniform circular motion is given as:
L = mvR
where m is the mass of the particle, v is its velocity, and R is the radius of the circular path.
When the frequency of particle's motion is doubled, the velocity of the particle also doubles since v = 2πfR. Therefore, the new angular momentum (L') is given as:
L' = m(2v)R = 2mvR = 2L
When the kinetic energy of the particle is halved, its velocity becomes √(1/2) times its original value since KE = (1/2)mv^2. Therefore, the new angular momentum (L'') is given as:
L'' = m(√(1/2)v)R = (1/√2)mvR = (1/√2)L
Therefore, the ratio of the new angular momentum to the original angular momentum is:
L''/L = (1/√2)L/L = L/√2L = (1/√2)
Simplifying, we get:
L'' = (1/√2)L = L/2
Hence, option D is the correct answer.
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A particle performs uniform circular motion with an angular momentum L. If the frequency of particles motion is doubled and its kinetic energy is halved, the angular momentum becomesa)2Lb)4Lc)L/2d)L/4Correct answer is option 'D'. Can you explain this answer?
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