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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 into a solid sphere. The moment of inertia of the sphere about its diameter as axis of rotation is :
- a)I
- b)2I/3
- c)I/5
- d)I/10
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
A circular disc of radius R and thickness R/6 has moment of inertia I ...
Understanding Moment of Inertia
The moment of inertia (I) of an object quantifies its resistance to rotational motion. For a circular disc and a solid sphere, the formulas differ based on their geometry.
Step 1: Moment of Inertia of the Disc
- A circular disc of radius R and thickness R/6 has a moment of inertia about its center (I) given by the formula:
I = (1/2) * M * R², where M is the mass of the disc.
- The volume (V) of the disc can be calculated as:
V = π * R² * (R/6) = (π/6) * R³.
- The density (ρ) of the disc is:
ρ = M/V.
- From density, we can express mass (M) in terms of volume and density.
Step 2: Melting and Recasting
- When the disc is melted and recast into a solid sphere, the mass remains the same.
- The volume of the sphere (V_sphere) is:
V_sphere = (4/3) * π * r³, where r is the radius of the sphere.
- Setting the volumes equal gives:
(π/6) * R³ = (4/3) * π * r³.
- From this, we can find the radius (r) of the sphere in terms of R.
Step 3: Moment of Inertia of the Sphere
- The moment of inertia (I_sphere) of a solid sphere about its diameter is given by:
I_sphere = (2/5) * M * r².
- Since the mass (M) is the same for both the disc and the sphere, substituting r into this formula allows us to express I_sphere in terms of I.
Final Calculation
- After substituting and simplifying, we find that:
I_sphere = I/5.
Thus, the correct answer is option 'C'.
The moment of inertia (I) of an object quantifies its resistance to rotational motion. For a circular disc and a solid sphere, the formulas differ based on their geometry.
Step 1: Moment of Inertia of the Disc
- A circular disc of radius R and thickness R/6 has a moment of inertia about its center (I) given by the formula:
I = (1/2) * M * R², where M is the mass of the disc.
- The volume (V) of the disc can be calculated as:
V = π * R² * (R/6) = (π/6) * R³.
- The density (ρ) of the disc is:
ρ = M/V.
- From density, we can express mass (M) in terms of volume and density.
Step 2: Melting and Recasting
- When the disc is melted and recast into a solid sphere, the mass remains the same.
- The volume of the sphere (V_sphere) is:
V_sphere = (4/3) * π * r³, where r is the radius of the sphere.
- Setting the volumes equal gives:
(π/6) * R³ = (4/3) * π * r³.
- From this, we can find the radius (r) of the sphere in terms of R.
Step 3: Moment of Inertia of the Sphere
- The moment of inertia (I_sphere) of a solid sphere about its diameter is given by:
I_sphere = (2/5) * M * r².
- Since the mass (M) is the same for both the disc and the sphere, substituting r into this formula allows us to express I_sphere in terms of I.
Final Calculation
- After substituting and simplifying, we find that:
I_sphere = I/5.
Thus, the correct answer is option 'C'.
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Community Answer
A circular disc of radius R and thickness R/6 has moment of inertia I ...
Moment of inertia of a disc,
I=1/2MR2
Disc is melted and recasted into a solid sphere.
I=1/2MR2
Disc is melted and recasted into a solid sphere.
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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 into a solid sphere. The moment of inertia of the sphere about its diameter as axis of rotation is :a)Ib)2I/3c)I/5d)I/10Correct answer is option 'C'. Can you explain this answer? for NEET 2025 is part of NEET preparation. The Question and answers have been prepared according to the NEET 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 into a solid sphere. The moment of inertia of the sphere about its diameter as axis of rotation is :a)Ib)2I/3c)I/5d)I/10Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for NEET 2025 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 into a solid sphere. The moment of inertia of the sphere about its diameter as axis of rotation is :a)Ib)2I/3c)I/5d)I/10Correct answer is option 'C'. Can you explain this answer?.
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 into a solid sphere. The moment of inertia of the sphere about its diameter as axis of rotation is :a)Ib)2I/3c)I/5d)I/10Correct answer is option 'C'. Can you explain this answer? for NEET 2025 is part of NEET preparation. The Question and answers have been prepared according to the NEET 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 into a solid sphere. The moment of inertia of the sphere about its diameter as axis of rotation is :a)Ib)2I/3c)I/5d)I/10Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for NEET 2025 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 into a solid sphere. The moment of inertia of the sphere about its diameter as axis of rotation is :a)Ib)2I/3c)I/5d)I/10Correct answer is option 'C'. 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 into a solid sphere. The moment of inertia of the sphere about its diameter as axis of rotation is :a)Ib)2I/3c)I/5d)I/10Correct answer is option 'C'. Can you explain this answer?, a detailed solution 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 into a solid sphere. The moment of inertia of the sphere about its diameter as axis of rotation is :a)Ib)2I/3c)I/5d)I/10Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of 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 into a solid sphere. The moment of inertia of the sphere about its diameter as axis of rotation is :a)Ib)2I/3c)I/5d)I/10Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
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