State and prove the law of conservation of energy.

Explanation

There is no change in the linear momentum of system of bodies as long as no net external force acts on them .
(ii) Let us prove the law of conservation of linear momentum with the following illustration :

(iii) Let two bodies A and B having masses `m_1` and `m_2` move eith initial velocity `u_1` and `u_2` in a straight line.
(iv) Let the velocity of the first body be higher than that of the second body.
i.e `u_1 gt u_2`
(v) During an interval of time t second , they tend to have a collision . After the impact, both of them move alon the same straight line with a velocity `v_1` and `v_2` respectively .
Force on body B due to A.
`F_(B)= (m_2[v_2-u_2])/(t)`
Force on body A due to B .
`F_(A) = (m_1[v_1 -u_1])/(t)`
By Newton .s III law of motion ,
Action force = Reaction force
`F_(A) = - F_(B)`
`(m_1[v_1-u_1])/(t)=- (m_2[v_2-u_2])/(t)`
`m_1 v_1 -m_2v_2 + m_2 mu_2`
`m_1v_1 + m_2v_2 = m_1u_1 + m_2u_2`
The above equation confirms in the absence of an external force, the algerbraic sum of the momentum after collision is numerically equal of the algebraic sum of the momentum beforce collision . Hence of the law of conservation linear momentum is proved .