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What is the moment of inertia of a solid sphere of mass 𝑀 and radius 𝑅 about an axis passing through its diameter?
The formula for the moment of inertia of a solid sphere about an axis through its diameter is 𝐼 = 2/5 𝑀𝑅². This is derived based on the sphere's uniform mass distribution and symmetry. This question related to Chapter 6 physics Class 11th NCERT. From the Chapter 6 System of Particles and RotationalRead more
The formula for the moment of inertia of a solid sphere about an axis through its diameter is 𝐼 = 2/5 𝑀𝑅². This is derived based on the sphere’s uniform mass distribution and symmetry. 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 position of the center of mass of a uniform rod of length 𝐿 and mass 𝑀?
For a uniform rod, the mass distribution is symmetric, so the center of mass lies at the geometrical center. Therefore, the center of mass is at the midpoint of the rod. This question related to Chapter 6 physics Class 11th NCERT. From the Chapter 6 System of Particles and Rotational Motion. Give anRead more
For a uniform rod, the mass distribution is symmetric, so the center of mass lies at the geometrical center. Therefore, the center of mass is at the midpoint of the rod.
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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A bomb is kept stationary at a point. It suddenly explodes into two fragments of masses 1 g and 3 g. The total K.E. of the fragments is 6.4 x 10⁴ J. What is the K.E. of the smaller fragment?
A stationary bomb breaks into two fragments with masses of 1 gram and 3 grams upon explosion. According to reports, the total kinetic energy of the fragments after the explosion is 64,000 joules. In this case, the kinetic energy of the lighter fragment can be found by taking into account principlesRead more
A stationary bomb breaks into two fragments with masses of 1 gram and 3 grams upon explosion. According to reports, the total kinetic energy of the fragments after the explosion is 64,000 joules. In this case, the kinetic energy of the lighter fragment can be found by taking into account principles from the law of conservation of momentum and that relating mass with kinetic energy.
In a system in which two objects collide or separate, the total momentum before and after the event is constant provided no external forces act on them. In this case, because the bomb was stationary before it exploded, the total momentum was zero, so the momentum of the fragments has to balance out after the explosion.
We know that the kinetic energy is distributed between the two fragments based on their respective masses, as deduced from the mass ratio of the fragments. The smaller fragment will have a proportionately smaller amount of kinetic energy compared to the larger fragment. Therefore, we can say that the kinetic energy of the smaller part will be 48,000 joules, and that of the larger part is going to be the rest after the explosion. Such a process explains how the principles of mass, momentum, and kinetic energy work hand in hand in an explosion.
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If the kinetic energy of a body becomes four times of its initial value, then new momentum will
When the kinetic energy of a body is increased, this affects the body's momentum. Kinetic energy is a measure of the amount of energy a body possesses due to its motion while momentum is the measure of motion in terms of mass and velocity. The two quantities are therefore related and changing one quRead more
When the kinetic energy of a body is increased, this affects the body’s momentum. Kinetic energy is a measure of the amount of energy a body possesses due to its motion while momentum is the measure of motion in terms of mass and velocity. The two quantities are therefore related and changing one quantity alters the other.
If the kinetic energy of a body becomes four times its initial value, then its momentum will double. This result follows from the mathematical relationship between kinetic energy and momentum. Kinetic energy increases with the square of velocity, but momentum increases linearly with velocity. Thus, when kinetic energy is multiplied by a factor of four, the velocity of the body increases by a factor of two, and momentum, being directly proportional to velocity, also doubles. For instance, let us consider a moving body whose kinetic energy is quadrupled by some external influence, such as an applied force. Its velocity will increase by the square root of four, that is, two, leading to a doubling of its momentum. This relationship shows how energy and motion are linked and how an increase in energy directly impacts the momentum of the body in a predictable way.
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A body of mass 𝑀 and radius 𝑅 is rolling without slipping. What is the ratio of its translational kinetic energy to rotational kinetic energy?
For rolling without slipping, v = Rω. Translational kinetic energy is 1/2Mv², and rotational kinetic energy is 1/2Iω². Using I = 2/5MR²(for a sphere), we find the ratio KEₜᵣₐₙₛₗₐₜᵢₒₙₐₗ : KEᵣₒₜₐₜᵢₒₙₐₗ = 2 : 1. This question related to Chapter 6 physics Class 11th NCERT. From the Chapter 6 System of PRead more
For rolling without slipping, v = Rω. Translational kinetic energy is 1/2Mv², and rotational kinetic energy is 1/2Iω². Using I = 2/5MR²(for a sphere), we find the ratio KEₜᵣₐₙₛₗₐₜᵢₒₙₐₗ : KEᵣₒₜₐₜᵢₒₙₐₗ = 2 : 1.
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/