Correct Answer - Option 3 : Force is proportional to the product of mass and acceleration
Explanation:
Newton’s Second Law of Motion:
According to newton's second law "The force acting to any object is directly proportional to the rate of change of linear momentum of the object."
Hence we can write:
\(Force \propto \frac{{change\;in\;momentum}}{{time}}\)
\(F\propto\frac{d(p)}{dt}\)
We know Momentum (p) = m × v
where m = Mass of the object, v = Velocity of an object
\(F\propto\frac{d(m\times v)}{dt}\)
\(F\propto (m\frac{d(v)}{dt}+v\frac{d(m)}{dt})\)
From the conservation of mass principle, Mass of the object (m) = constant
so \(\frac{dm}{dt}=0\)
∴ \(F\propto m\frac{d(v)}{dt}\)
We know, Acceleration is the rate of change of velocity so, \(a=\frac{dv}{dt}\)
∴\(F\propto (ma)\)
Hence it is clear from newton's 2nd law that force is proportional to the product of mass and acceleration.
Newton’s First law:
A body continues to be in its state of rest or of uniform motion along a straight line unless it is acted upon by some external force to change the state.
- If no net force acts on a body, then the velocity of the body cannot change i.e. the body cannot accelerate.
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Newton’s first law defines inertia and is rightly called the law of inertia.
Newton’s Third Law:
To every action, there is always an equal (in magnitude) and opposite (in direction) reaction.
- When a body exerts a force on any other body, the second body also exerts an equal and opposite force on the first.
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Forces in nature always occur in pairs. A single isolated force is not possible.
