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The rate of change of momentum of an object is proportional to:
- a)Mass of the body
- b)Velocity of the body
- c)Net force applied on the body
- d)None of these
Correct answer is option 'C'. Can you explain this answer?
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The rate of change of momentum of an object is proportional to:a) Mas...
According to Newton's second law, The rate of change of linear momentum of a body is directly proportional to the external force applied on the body , and takes place always in the direction of the force applied. So the rate of change of momentum is Force i.e. Newton's second law helps us to derive an equation for force.
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The rate of change of momentum of an object is proportional to:a) Mas...
The rate of change of momentum of an object is proportional to the net force applied on the body. This is explained by Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.
Let's break down the explanation in detail:
- Newton's Second Law:
- According to Newton's second law, the acceleration of an object is directly proportional to the net force applied on it. Mathematically, this can be represented as:
F = ma
where F is the net force, m is the mass of the object, and a is the acceleration.
- Definition of Momentum:
- Momentum is defined as the product of an object's mass and velocity. Mathematically, momentum (p) can be expressed as:
p = mv
where p is the momentum, m is the mass of the object, and v is the velocity.
- Rate of Change of Momentum:
- The rate of change of momentum of an object is given by the formula:
dp/dt = m * dv/dt
where dp/dt represents the rate of change of momentum, m is the mass of the object, and dv/dt is the rate of change of velocity.
- Relation to Net Force:
- By substituting acceleration (a) for dv/dt in the formula for rate of change of momentum, we get:
dp/dt = m * a
Since acceleration is directly proportional to the net force applied on the object (F = ma), we can conclude that the rate of change of momentum is proportional to the net force.
Therefore, the correct answer to the question is option 'C': Net force applied on the body.
Let's break down the explanation in detail:
- Newton's Second Law:
- According to Newton's second law, the acceleration of an object is directly proportional to the net force applied on it. Mathematically, this can be represented as:
F = ma
where F is the net force, m is the mass of the object, and a is the acceleration.
- Definition of Momentum:
- Momentum is defined as the product of an object's mass and velocity. Mathematically, momentum (p) can be expressed as:
p = mv
where p is the momentum, m is the mass of the object, and v is the velocity.
- Rate of Change of Momentum:
- The rate of change of momentum of an object is given by the formula:
dp/dt = m * dv/dt
where dp/dt represents the rate of change of momentum, m is the mass of the object, and dv/dt is the rate of change of velocity.
- Relation to Net Force:
- By substituting acceleration (a) for dv/dt in the formula for rate of change of momentum, we get:
dp/dt = m * a
Since acceleration is directly proportional to the net force applied on the object (F = ma), we can conclude that the rate of change of momentum is proportional to the net force.
Therefore, the correct answer to the question is option 'C': Net force applied on the body.
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