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If momentum of a body is increased by 2% then by how much it's Kinetic energy will get changed?
Most Upvoted Answer
If momentum of a body is increased by 2% then by how much it's Kinetic...
Let
P=100
Pnew=100+2=102
change in kinetic energy
K.Enew-K.E/K.E *100 as(P^2/2m =K.E)
=(Pnew^2/2m) -(P^2/2m)/p^2/2m *100
=102^2-100^2/100
=4.04 percent
P=100
Pnew=100+2=102
change in kinetic energy
K.Enew-K.E/K.E *100 as(P^2/2m =K.E)
=(Pnew^2/2m) -(P^2/2m)/p^2/2m *100
=102^2-100^2/100
=4.04 percent
Community Answer
If momentum of a body is increased by 2% then by how much it's Kinetic...
Answer:
To understand how the kinetic energy of a body changes when its momentum is increased by 2%, we need to first understand the relationship between momentum and kinetic energy.
Momentum:
Momentum is defined as the product of an object's mass and its velocity. It is a vector quantity, which means it has both magnitude and direction. The formula for momentum is:
Momentum = mass × velocity
Kinetic Energy:
Kinetic energy is the energy possessed by an object due to its motion. It depends on the mass and velocity of the object. The formula for kinetic energy is:
Kinetic Energy = 1/2 × mass × velocity^2
Relationship between Momentum and Kinetic Energy:
It can be observed that both momentum and kinetic energy depend on the mass and velocity of an object. However, they are not directly proportional to each other. While momentum depends linearly on velocity, kinetic energy depends on the square of velocity.
Calculation:
Let's assume the initial momentum of the body is P and the initial kinetic energy is KE. When the momentum is increased by 2%, the new momentum becomes P + 0.02P = 1.02P.
To find the new kinetic energy, we can use the formula for kinetic energy and substitute the new momentum:
New Kinetic Energy = 1/2 × mass × (1.02P/ mass)^2
= 1/2 × (1.02P)^2
= 1/2 × 1.0404P^2
= 0.5202P^2
Therefore, the kinetic energy of the body will change by a factor of 0.5202 when the momentum is increased by 2%.
Explanation:
When the momentum of a body increases, it means that either its mass or velocity or both have increased. As kinetic energy depends on the square of velocity, any change in velocity will have a greater impact on kinetic energy compared to the change in mass.
In this case, when the momentum is increased by 2%, the new kinetic energy is found to be 0.5202 times the initial kinetic energy. This means that the kinetic energy decreases by 47.98% (1 - 0.5202) when the momentum is increased by 2%.
Summary:
When the momentum of a body is increased by 2%, the kinetic energy of the body will decrease by 47.98%. This is because kinetic energy depends on the square of velocity, and any change in velocity will have a greater impact on kinetic energy compared to the change in mass.
To understand how the kinetic energy of a body changes when its momentum is increased by 2%, we need to first understand the relationship between momentum and kinetic energy.
Momentum:
Momentum is defined as the product of an object's mass and its velocity. It is a vector quantity, which means it has both magnitude and direction. The formula for momentum is:
Momentum = mass × velocity
Kinetic Energy:
Kinetic energy is the energy possessed by an object due to its motion. It depends on the mass and velocity of the object. The formula for kinetic energy is:
Kinetic Energy = 1/2 × mass × velocity^2
Relationship between Momentum and Kinetic Energy:
It can be observed that both momentum and kinetic energy depend on the mass and velocity of an object. However, they are not directly proportional to each other. While momentum depends linearly on velocity, kinetic energy depends on the square of velocity.
Calculation:
Let's assume the initial momentum of the body is P and the initial kinetic energy is KE. When the momentum is increased by 2%, the new momentum becomes P + 0.02P = 1.02P.
To find the new kinetic energy, we can use the formula for kinetic energy and substitute the new momentum:
New Kinetic Energy = 1/2 × mass × (1.02P/ mass)^2
= 1/2 × (1.02P)^2
= 1/2 × 1.0404P^2
= 0.5202P^2
Therefore, the kinetic energy of the body will change by a factor of 0.5202 when the momentum is increased by 2%.
Explanation:
When the momentum of a body increases, it means that either its mass or velocity or both have increased. As kinetic energy depends on the square of velocity, any change in velocity will have a greater impact on kinetic energy compared to the change in mass.
In this case, when the momentum is increased by 2%, the new kinetic energy is found to be 0.5202 times the initial kinetic energy. This means that the kinetic energy decreases by 47.98% (1 - 0.5202) when the momentum is increased by 2%.
Summary:
When the momentum of a body is increased by 2%, the kinetic energy of the body will decrease by 47.98%. This is because kinetic energy depends on the square of velocity, and any change in velocity will have a greater impact on kinetic energy compared to the change in mass.
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If momentum of a body is increased by 2% then by how much it's Kinetic energy will get changed?
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If momentum of a body is increased by 2% then by how much it's Kinetic energy will get changed? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about If momentum of a body is increased by 2% then by how much it's Kinetic energy will get changed? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If momentum of a body is increased by 2% then by how much it's Kinetic energy will get changed?.
If momentum of a body is increased by 2% then by how much it's Kinetic energy will get changed? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about If momentum of a body is increased by 2% then by how much it's Kinetic energy will get changed? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If momentum of a body is increased by 2% then by how much it's Kinetic energy will get changed?.
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