Question

hii friends what is second law of newton

Answer 1

$\textbf{NEWTON'S SECOND LAW}$

According to it the rate of change of linear momentum of a body is directly proportional to the applied external force.
___________________________________

$\textbf{DERIVATION}$

Force = (Change in momentum / Time)

Now, we know that;

Momentum = Product of mass and velocity of the body. i.e.

P = mv

Let us consider that a body of mass (m) is moving with a initial velocity (u) and with final velocity (v) in time (t)

Initial momentum = p1 = mu

Final momentum = p2 = mv

Then,

Change in momentum of the body = p2 - p1

F = mv -mu

F = [m (v - u) / t] .........(1)

As we know that,

a = [(v - u) / t] ...........(2)

Put the value of (2) in (1)

Then,

$\textbf{F = ma}$
__________________________________

OR

Rate of change of linear momentum is directly proportional to force.

So,

F α dp/dt

F = k dp/dt

Now,

p (momentum) = mv

So,

F = k d(mv)/dt

F = k md(v)/dt

F = k ma

[As dv/dt = a]

Experimentally k =1

$\textbf{F = ma}$
_________________________________