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A wheel is rotating freely with an angular speed ω on a shaft. The moment of inertia of the wheel is I and the moment of inertia of the shaft is negligible. Another wheel of moment of inertia 3I initially at rest is suddenly coupled to the same shaft. The resultant fractional loss in the kinetic energy of the system is:
  • a)
    5/6
  • b)
    1/4
  • c)
    0
  • d)
    3/4
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
A wheel is rotating freely with an angular speed ω on a shaft. The mo...
From angular momentum conservation
Loss of kinetic energy
Fractional loss = 3/4
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Community Answer
A wheel is rotating freely with an angular speed ω on a shaft. The mo...
Given information:
- A wheel is rotating freely with an angular speed ω on a shaft.
- The moment of inertia of the wheel is I.
- The moment of inertia of the shaft is negligible.
- Another wheel of moment of inertia 3I is initially at rest.
- The second wheel is suddenly coupled to the same shaft.

Objective:
To calculate the fractional loss in the kinetic energy of the system.

Explanation:
1. Initial Kinetic Energy:
The initial kinetic energy of the system can be calculated using the formula:

KE1 = 0.5 * I * ω^2

Since the first wheel is rotating freely, it has kinetic energy associated with its angular speed.

2. Final Kinetic Energy:
After the second wheel is coupled to the shaft, the moment of inertia of the system becomes 4I (I for the first wheel and 3I for the second wheel).

The final angular speed of the system can be calculated using the principle of conservation of angular momentum.

Initial angular momentum = Final angular momentum

(I * ω) + (0 * 0) = (4I * ω_f)

Simplifying the equation, we get:

ω_f = ω/4

The final kinetic energy of the system can be calculated using the formula:

KE2 = 0.5 * (4I) * (ω/4)^2

Simplifying the equation, we get:

KE2 = 0.5 * I * ω^2 * (1/8)

3. Fractional Loss in Kinetic Energy:
The fractional loss in kinetic energy can be calculated using the formula:

Fractional Loss = (KE1 - KE2) / KE1

Substituting the values of KE1 and KE2, we get:

Fractional Loss = (0.5 * I * ω^2 - 0.5 * I * ω^2 * (1/8)) / (0.5 * I * ω^2)

Simplifying the equation, we get:

Fractional Loss = (1 - 1/8)

Fractional Loss = 7/8

Therefore, the fractional loss in the kinetic energy of the system is 7/8, which is approximately 0.875 or 0.88.

Answer:
The correct option is (d) 3/4.
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A wheel is rotating freely with an angular speed ω on a shaft. The moment of inertia of the wheel is I and the moment of inertia of the shaft is negligible. Another wheel of moment of inertia 3I initially at rest is suddenly coupled to the same shaft. The resultant fractional loss in the kinetic energy of the system is:a)5/6b)1/4c)0d)3/4Correct answer is option 'D'. Can you explain this answer?
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A wheel is rotating freely with an angular speed ω on a shaft. The moment of inertia of the wheel is I and the moment of inertia of the shaft is negligible. Another wheel of moment of inertia 3I initially at rest is suddenly coupled to the same shaft. The resultant fractional loss in the kinetic energy of the system is:a)5/6b)1/4c)0d)3/4Correct answer is option 'D'. 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 A wheel is rotating freely with an angular speed ω on a shaft. The moment of inertia of the wheel is I and the moment of inertia of the shaft is negligible. Another wheel of moment of inertia 3I initially at rest is suddenly coupled to the same shaft. The resultant fractional loss in the kinetic energy of the system is:a)5/6b)1/4c)0d)3/4Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A wheel is rotating freely with an angular speed ω on a shaft. The moment of inertia of the wheel is I and the moment of inertia of the shaft is negligible. Another wheel of moment of inertia 3I initially at rest is suddenly coupled to the same shaft. The resultant fractional loss in the kinetic energy of the system is:a)5/6b)1/4c)0d)3/4Correct answer is option 'D'. Can you explain this answer?.
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