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A uniform circular disc of mass 200 g and radius 4 cm is rotated about one of its diameter at an angular speed of 10 rad/s. The ratio of its kinetic energy to its angular momentum about the axis of rotation is
- a)5
- b)10
- c)1
- d)20
Correct answer is option 'A'. Can you explain this answer?
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A uniform circular disc of mass 200 g and radius 4 cm is rotated about...
The moment of inertia of the circular disc about is diametter is
and the angular momentum about the axis of rotation is
and the angular momentum about the axis of rotation is
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A uniform circular disc of mass 200 g and radius 4 cm is rotated about...
Given data:
Mass of the disc (m) = 200 g = 0.2 kg
Radius of the disc (r) = 4 cm = 0.04 m
Angular speed of rotation (ω) = 10 rad/s
We need to find the ratio of the kinetic energy (KE) to the angular momentum (L) about the axis of rotation.
1. Calculating the moment of inertia (I) of the disc:
The moment of inertia of a uniform circular disc rotating about an axis perpendicular to its plane and passing through its center is given by the formula:
I = (1/4) * m * r^2
Substituting the given values:
I = (1/4) * 0.2 kg * (0.04 m)^2
I = 0.0016 kg·m^2
2. Calculating the kinetic energy (KE) of the disc:
The kinetic energy of a rotating object is given by the formula:
KE = (1/2) * I * ω^2
Substituting the given values:
KE = (1/2) * 0.0016 kg·m^2 * (10 rad/s)^2
KE = 0.08 J
3. Calculating the angular momentum (L) of the disc:
The angular momentum of a rotating object is given by the formula:
L = I * ω
Substituting the given values:
L = 0.0016 kg·m^2 * 10 rad/s
L = 0.016 kg·m^2/s
4. Calculating the ratio of kinetic energy to angular momentum:
Ratio = KE / L
Ratio = 0.08 J / 0.016 kg·m^2/s
Ratio = 5 J·s/J·s
Ratio = 5
Hence, the ratio of the kinetic energy to the angular momentum about the axis of rotation is 5, which corresponds to option A.
Mass of the disc (m) = 200 g = 0.2 kg
Radius of the disc (r) = 4 cm = 0.04 m
Angular speed of rotation (ω) = 10 rad/s
We need to find the ratio of the kinetic energy (KE) to the angular momentum (L) about the axis of rotation.
1. Calculating the moment of inertia (I) of the disc:
The moment of inertia of a uniform circular disc rotating about an axis perpendicular to its plane and passing through its center is given by the formula:
I = (1/4) * m * r^2
Substituting the given values:
I = (1/4) * 0.2 kg * (0.04 m)^2
I = 0.0016 kg·m^2
2. Calculating the kinetic energy (KE) of the disc:
The kinetic energy of a rotating object is given by the formula:
KE = (1/2) * I * ω^2
Substituting the given values:
KE = (1/2) * 0.0016 kg·m^2 * (10 rad/s)^2
KE = 0.08 J
3. Calculating the angular momentum (L) of the disc:
The angular momentum of a rotating object is given by the formula:
L = I * ω
Substituting the given values:
L = 0.0016 kg·m^2 * 10 rad/s
L = 0.016 kg·m^2/s
4. Calculating the ratio of kinetic energy to angular momentum:
Ratio = KE / L
Ratio = 0.08 J / 0.016 kg·m^2/s
Ratio = 5 J·s/J·s
Ratio = 5
Hence, the ratio of the kinetic energy to the angular momentum about the axis of rotation is 5, which corresponds to option A.
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A uniform circular disc of mass 200 g and radius 4 cm is rotated about one of its diameter at an angular speed of 10 rad/s. The ratio of its kinetic energy to its angular momentum about the axis of rotation isa)5b)10c)1d)20Correct answer is option 'A'. Can you explain this answer?
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A uniform circular disc of mass 200 g and radius 4 cm is rotated about one of its diameter at an angular speed of 10 rad/s. The ratio of its kinetic energy to its angular momentum about the axis of rotation isa)5b)10c)1d)20Correct answer is option 'A'. Can you explain this answer? for IIT JAM 2024 is part of IIT JAM preparation. The Question and answers have been prepared according to the IIT JAM exam syllabus. Information about A uniform circular disc of mass 200 g and radius 4 cm is rotated about one of its diameter at an angular speed of 10 rad/s. The ratio of its kinetic energy to its angular momentum about the axis of rotation isa)5b)10c)1d)20Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for IIT JAM 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A uniform circular disc of mass 200 g and radius 4 cm is rotated about one of its diameter at an angular speed of 10 rad/s. The ratio of its kinetic energy to its angular momentum about the axis of rotation isa)5b)10c)1d)20Correct answer is option 'A'. Can you explain this answer?.
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