State Newton's second law of motion. How it helps us to measure force ? State its CGS and SI units.

Explanation

Newton.s second law: It states that time rate of change of momentum of a body is directly proportional to the applied force and the change takes place in the direction of applied force.
Mathematically, `(dvecp)/(dt) prop vecF`
Where `vecF` is the applied force, `vecF= (dvecp)/(dt)`
Since `vecp= mvecv` therefore `vecF= (d)/(dt)(mvecv)` or `vecF= m(dvecv)/(dt)` or `vecF= mveca`
Magnitude of the force is given by F = ma ....(i)
Hence, force can be calculated by using equation (i). It means, second law of motion gives measure of force.
i) Absolute unit of force: A force is said to be absolute unit of force, if it produces unit acceleration in unit mass of body.
a) CGS system: Unit of force is dyne.
we know that, F= ma
`1 "dyne" = 1 g xx cm s^(-2)`.
Thus, force is I dyne, if it produces `1 cm s^(-2)` acceleration in a body of mass 1 g.
b) SI system: Unit of force is newton (N).
F= ma
1 newton =` kg m s^(-2)`
Thus, a force is 1 newton, if it produces `1 m s^(-2)` acceleration in a body of mass 1kg.
ii) Gravitational unit of force
a) SI system: Unit of force is kilogram weight. It is that force, which produces an acceleration of `9.8 m s^(-2)` in a mass of 1 kg. i. e., 1 kg wt (kgf) = 9.8 N
b) CGS system: Unit of force is gram weight. It is that force, which produces an acceleration of `980 cm s^(-2)` in a mass of 1g. i.e., lg wt (gf) = 980 dyne.