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A solid sphere rolls without slipping down an inclined plane. What fraction of its total energy is rotational kinetic energy?
When a solid sphere rolls without slipping down an inclined plane, its total energy is distributed between translational kinetic energy and rotational kinetic energy. The fraction of its total energy that is rotational kinetic energy can be derived as follows: 1. Total Energy (E): E = KEₜᵣₐₙₛₗₐₜᵢₒₙₐRead more
When a solid sphere rolls without slipping down an inclined plane, its total energy is distributed between translational kinetic energy and rotational kinetic energy. The fraction of its total energy that is rotational kinetic energy can be derived as follows:
1. Total Energy (E):
E = KEₜᵣₐₙₛₗₐₜᵢₒₙₐₗ + KEᵣₒₜₐₜᵢₒₙₐₗ
2. Translational Kinetic Energy:
KEₜᵣₐₙₛₗₐₜᵢₒₙₐₗ = 1/2Mv², where M is the mass and v is the velocity of the center of mass.
3. Rotational Kinetic Energy:
KEᵣₒₜₐₜᵢₒₙₐₗ = 1/2Iω², where I is the moment of inertia and ω is the angular velocity. For a solid sphere, I = 2/5MR² and ω = v/R. Substituting ω, KEᵣₒₜₐₜᵢₒₙₐₗ = 1/2.2/5MR². v²/R² = 1/5Mv².
4. Total Energy Expression:
E = 1/2Mv² + 1/5Mv² = 7/10Mv².
5. Fraction of Rotating Energy:
Fraction of Rotation Energy = KEᵣₒₜₐₜᵢₒₙₐₗ/E = (1/5Mv²) / (7/10 Mv²) = 2/7.
The fraction of the total energy that is rotational kinetic energy is 2/7.
This question related to Chapter 6 physics Class 11th NCERT. From the Chapter 6 System of Particles and Rotational Motion. Give answer according to your understanding.
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What is the physical significance of the radius of gyration?
The radius of gyration 𝑘 gives an equivalent distance from the axis at which the entire mass of the body can be assumed to be concentrated to produce the same moment of inertia. This question related to Chapter 6 physics Class 11th NCERT. From the Chapter 6 System of Particles and Rotational Motion.Read more
The radius of gyration 𝑘 gives an equivalent distance from the axis at which the entire mass of the body can be assumed to be concentrated to produce the same moment of inertia.
This question related to Chapter 6 physics Class 11th NCERT. From the Chapter 6 System of Particles and Rotational Motion. Give answer according to your understanding.
For more please visit here:
See lesshttps://www.tiwariacademy.com/ncert-solutions/class-11/physics/chapter-6/
If the net external force acting on a system of particles is zero, what can be said about the motion of its center of mass?
If the net external force is zero, the acceleration of the center of mass is also zero. Hence, it moves with constant velocity according to Newton’s first law of motion. This question related to Chapter 6 physics Class 11th NCERT. From the Chapter 6 System of Particles and Rotational Motion. Give anRead more
If the net external force is zero, the acceleration of the center of mass is also zero. Hence, it moves with constant velocity according to Newton’s first law of motion. This question related to Chapter 6 physics Class 11th NCERT. From the Chapter 6 System of Particles and Rotational Motion. Give answer according to your understanding.
For more please visit here:
See lesshttps://www.tiwariacademy.com/ncert-solutions/class-11/physics/chapter-6/
Define a wavefront. Use Huygen’s principle to verify the laws of refraction.
A wavefront is the locus of points vibrating in phase, representing the crest of a wave at a given time. Using Huygen’s principle, each point on the wavefront acts as a secondary wavelet source. At a boundary between two media, constructing tangents to these wavelets shows how wave direction changesRead more
A wavefront is the locus of points vibrating in phase, representing the crest of a wave at a given time.
Using Huygen’s principle, each point on the wavefront acts as a secondary wavelet source. At a boundary between two media, constructing tangents to these wavelets shows how wave direction changes, verifying Snell’s law: sin i/sin r = v₁/v₂ .
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See lesshttps://www.tiwariacademy.com/ncert-solutions/class-12/physics/chapter-10/
Discuss with the students, how they felt after the practice.
After completing the practices, hold a discussion with students to reflect on their experiences. Ask them how they felt about mindful eating, serving others, and avoiding distractions during meals. Highlight the benefits they noticed, such as stronger family connections, improved focus, or a sense oRead more
After completing the practices, hold a discussion with students to reflect on their experiences. Ask them how they felt about mindful eating, serving others, and avoiding distractions during meals. Highlight the benefits they noticed, such as stronger family connections, improved focus, or a sense of fulfillment. Encourage them to share personal insights and emotions, fostering a deeper understanding of how these practices contribute to emotional well-being, gratitude, and a more harmonious lifestyle.
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