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A mass is whirled in a circular path with constant angular velocity and its angular momentum is L. If the string is now halved keeping the angular velocity the same, the angular momentum is
- a)L/4
- b)L/2
- c)L
- d)2L
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
A mass is whirled in a circular path with constant angular velocity a...
Explanation:
Angular Momentum:
- Angular momentum (L) of an object moving in a circular path is given by the product of its moment of inertia (I) and angular velocity (ω), i.e., L = I * ω.
Effect of Halving the String:
- When the string is halved, the moment of inertia (I) of the mass decreases by a factor of 4 (since I is directly proportional to the square of the radius).
- At the same time, the angular velocity (ω) remains constant.
- Therefore, the new angular momentum (L') after halving the string is given by L' = (1/4) * I * ω = (1/4) * L = L/4.
Conclusion:
- The new angular momentum after halving the string is one-fourth of the original angular momentum.
- Hence, the correct answer is option 'A' - L/4.
Angular Momentum:
- Angular momentum (L) of an object moving in a circular path is given by the product of its moment of inertia (I) and angular velocity (ω), i.e., L = I * ω.
Effect of Halving the String:
- When the string is halved, the moment of inertia (I) of the mass decreases by a factor of 4 (since I is directly proportional to the square of the radius).
- At the same time, the angular velocity (ω) remains constant.
- Therefore, the new angular momentum (L') after halving the string is given by L' = (1/4) * I * ω = (1/4) * L = L/4.
Conclusion:
- The new angular momentum after halving the string is one-fourth of the original angular momentum.
- Hence, the correct answer is option 'A' - L/4.
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Community Answer
A mass is whirled in a circular path with constant angular velocity a...
L = mr2 ω. For given m and ω, L ∝ r2. If r is halved, the angular momentum L becomes one-fourth.
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A mass is whirled in a circular path with constant angular velocity and its angular momentum is L. If the string is now halved keeping the angular velocity the same, the angular momentum isa)L/4b)L/2c)Ld)2LCorrect answer is option 'A'. Can you explain this answer?
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