Question

state the state and explain the Newton's second law of motion also define Momentum with derivation​

Answer 1

$\bold{\underline{ANSWER}}$

$\bold{\underline {Newton's\ second\ law\ of\ motion}}$

$\implies$ According to this law, the rate of change of momentum of a body per unit time is directly proportional to the unbalanced force acting on the body.

$\implies$Which means F is directly proportional to $\dfrac {p}{t}$

Equation for the second law is -

$\boxed{\bold {F = ma}}$

$\bold {\underline {Derivation\ for\ the\ second\ law}}$

$\implies}$Consider a body of mass m moving with initial velocity u. Let a force F acts on the body for time t.

Initial momentum = mu

Final momentum = mv

Change in momentum = mu - mv
= m(v - u)

Time taken = t

Rate of change of momentum

= $\dfrac {change\ of\ momentum}{time\ taken}$

= $\dfrac {m (v - u)}{t}$

F (directly proportional) $\dfrac {m (v - u)}{t}$ ...( 1 )

Since v = u + at

$\dfrac {(v - u)}{t}$ = a

Therefore, equation 1 can be written as

F = k ma ..... ( 2 )

Where k is constant of proportionality

F = 1 unit
m = 1 unit
a = 1 unit

Then from eq. ( 2 )
K = 1

Put this value of k in eq. ( 2 )

So, $\huge\bold {F = ma}$

$\bold {\underline{Momentum}}$

$\implies$ Momentum is known as the product of mass and velocity

• Momentum = mass × velocity

• It is denoted by P

• Momentum is a vector quantity

• S.I. unit of momentum = kg m/s

• C.G.S. system = g cm/s

• Other unit = N/s

$\bold {\underline {Derivation}}$

$\implies$Momentum = mass × velocity

• Momentum = P

• Mass = m

• Velocity = v

$\boxed{\bold{ P = m v}}$