Question

derive the relation between force acting on a body of mass and producing acceleration ​

Answer 1

Given:

A force acting on a body of mass and producing acceleration ​

To Find:

If F is the force acting on the body  of mass m and acceleration a, then

                               F = ma          

Solution:

From Newton's second law,   

                                     F ∝ $\frac{dp}{dt}$              . . .(1)

Here, p = momentum of the body

Let, v be the velocity of the particle

From eq.(1)

                                    F ∝ $m\frac{dv}{dt}$           . . .(2)

Since, $\frac{dv}{dt} = a$ eq.(2) becomes

                                    F ∝$ma$             . . .(3)

If k is the proportionality

                                    F = kma           . . .(4)

If 1 N force is applied to a body of mass 1kg to produce an acceleration of $1ms^{-2}$ magnitude of k becomes 1.

Hence, eq.(4) =>

                                    F = ma

∴The relation between force acting on a body of mass and producing acceleration is, F = ma