Question

The ratio of force and acceleration is
A. Mass
B. Impulse
C. Momentum
D. None of these

Answer 1

Hint: In physics, force is defined as a push or pull. Newton's second law defines force as the rate of change of momentum. Acceleration is the rate of change of velocity. Here, we will discuss the relation between force and acceleration


Complete step by step solution:
According to newton's second law of motion, the rate of change of momentum equals the force applied i.e.
$f = \dfrac{{dp}}{{dt}}$
We also know that momentum is the product of mass and velocity of the object,i.e.
$p = mv$
Here, $p$ is momentum, $m$ is mass, and $v$ is the velocity of the object.
Let us now put these values in the above equation.
$f = \dfrac{{d\left( {mv} \right)}}{{dt}}$
  At lower speed, the mass of an object is constant. So, we can take mass which is constant out of the differentiation.
$f = m\dfrac{{dv}}{{dt}}$
Now we know that the rate of change of velocity is acceleration. Therefore, we can write the above expression as below.
$f = ma$
Now, let us find the ratio of force and acceleration.
$\dfrac{f}{a} = m$
Therefore, we can say that the ratio of force and acceleration gives the mass of the object.
Hence, option (A) mass is correct.

Note:
The momentum of an object depends on the mass.
If the same force is acting on two objects of different masses, then the momentum gained by the lighter object will be higher than the momentum gained by the heavier object.
Also, the velocity achieved by a lighter object will be higher than the heavier object.
We define Impulse as when a large force acts on an object for a small interval of time.