(a) State Newton's second law of motion . Hence derive the equation of motion F = ma from it .
(b) A body is moving along a circular path such that its speed always remains constant .

Explanation

(a)Newton.s Second of motion : The rate of change of momentum of a body is dimensional proportional to the external force applied and takes place in the same direction ".
To show F = ma : Let a body of mass m moving with a velocity v under the action of an extremely force F in the direction of velocity .
Momentum .P. of a body is the product of the mass and velocity v .
P = mv ....(1)
According to Newton.s second law of motion , we have
`(dp)/(dt) alpha F,` where F = external force
(or) `F = K (dp)/(dt) ........(2)`
From equations (1) and (2) we have
` F = K (d(mv))/(dt) = K.m (dv)/(dt) = Kma .......(3)`
Since the rate of change of velocity `(dv)/(dt)` is the acceleration .a. of the body .
In SI system the unit of force is Newton and is defined as that force which when acting on a body mass 1 kg produces in it an acceleration of `1 ms^(-2)` .
i.e ., from equation (3),
If F=1 , m = 1 and a = 1 we get K= 1
Hence `F= (dp)/(dt) = ma`
` :. F = ma `
(b) Suppose a body is moving along a circular part though its speed always remains constant its velocity changes at every point and resultant force acts on the body .