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A circular disc of radius r and thickness r/6 has moment of inertia I about an axis passing through its centre and perpendicular to its plane. It is melted and recasted to a solid sphere. The moment of inertia of the sphere about its diameter as axis of rotation is
  • a)
    I/2
  • b)
    2I/11
  • c)
    I/10
  • d)
    I/5
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
A circular disc of radius r and thickness r/6 has moment of inertia I ...
Volume oc circular disc = surface of area x thickness

The mass of the circular disc and sphere are the same

where R is the radius of the sphere,

Moment of interia of a circluar disc

Moment of interia of solid sphere
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Community Answer
A circular disc of radius r and thickness r/6 has moment of inertia I ...


Given Data:
- Radius of circular disc, r
- Thickness of circular disc, r/6
- Moment of inertia of circular disc about its center and perpendicular axis, I

Calculating Moment of Inertia of the Solid Sphere:
- The moment of inertia of a solid sphere about its diameter is given by the formula: I = (2/5) * M * R^2, where M is the mass of the sphere and R is the radius of the sphere.
- The volume of the circular disc is equal to the volume of the solid sphere, as it is melted and recasted. Hence, the mass of the sphere will be equal to the mass of the circular disc.
- Volume of circular disc = π * r^2 * (r/6) = π * r^3 / 6
- Volume of solid sphere = (4/3) * π * R^3, where R is the radius of the sphere
- Equating the volumes: (4/3) * π * R^3 = π * r^3 / 6
- Solving for R: R = (r/6) * (3/2)^(1/3)

Substituting in the Moment of Inertia formula:
- I_sphere = (2/5) * M * R^2
- Substituting M = π * r^3 / 6 and R = (r/6) * (3/2)^(1/3) into the formula
- I_sphere = (2/5) * (π * r^3 / 6) * [(r/6) * (3/2)^(1/3)]^2
- Simplifying the expression gives: I_sphere = I/5

Therefore, the moment of inertia of the sphere about its diameter as the axis of rotation is I/5, which is option 'D'.
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A circular disc of radius r and thickness r/6 has moment of inertia I about an axis passing through its centre and perpendicular to its plane. It is melted and recasted to a solid sphere. The moment of inertia of the sphere about its diameter as axis of rotation isa)I/2b)2I/11c)I/10d)I/5Correct answer is option 'D'. Can you explain this answer?
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A circular disc of radius r and thickness r/6 has moment of inertia I about an axis passing through its centre and perpendicular to its plane. It is melted and recasted to a solid sphere. The moment of inertia of the sphere about its diameter as axis of rotation isa)I/2b)2I/11c)I/10d)I/5Correct answer is option 'D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A circular disc of radius r and thickness r/6 has moment of inertia I about an axis passing through its centre and perpendicular to its plane. It is melted and recasted to a solid sphere. The moment of inertia of the sphere about its diameter as axis of rotation isa)I/2b)2I/11c)I/10d)I/5Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A circular disc of radius r and thickness r/6 has moment of inertia I about an axis passing through its centre and perpendicular to its plane. It is melted and recasted to a solid sphere. The moment of inertia of the sphere about its diameter as axis of rotation isa)I/2b)2I/11c)I/10d)I/5Correct answer is option 'D'. Can you explain this answer?.
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