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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.
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Is the law of conservation of energy obeyed by interference phenomenon of light?
Yes, the law of conservation of energy is obeyed in the interference of light. While energy is redistributed between constructive and destructive interference regions, the total energy across the entire interference pattern remains constant. No energy is created or destroyed in the process. For moreRead more
Yes, the law of conservation of energy is obeyed in the interference of light. While energy is redistributed between constructive and destructive interference regions, the total energy across the entire interference pattern remains constant. No energy is created or destroyed in the process.
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Which of the following is true?
In the case of collisions, momentum and kinetic energy behave differently. Momentum is a fundamental property of motion, which is always conserved in all types of collisions provided no external forces act on the system. This universal principle applies to both elastic and inelastic collisions. KineRead more
In the case of collisions, momentum and kinetic energy behave differently. Momentum is a fundamental property of motion, which is always conserved in all types of collisions provided no external forces act on the system. This universal principle applies to both elastic and inelastic collisions.
Kinetic energy, however, is not conserved. It is conserved only in elastic collisions, where there is no loss of energy to heat, sound, or deformation. In such cases, the total kinetic energy of the system before and after the collision remains the same. Elastic collisions typically occur at a microscopic level, such as between gas particles, where energy is perfectly transferred between colliding objects.
In inelastic collisions, kinetic energy is not conserved. A part of it is converted into other forms of energy, such as heat, sound, or potential energy due to deformation of the colliding objects. Inelastic collisions are very common in everyday life, like a car crash, where deformation of the vehicles and heat generation result in loss of kinetic energy.
Thus, momentum conservation is a universal law of all collisions, whereas the former depends on the nature of the collision and points out to be an important distinction between the two.
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