Question

State and proove law of conservation of momentum

Answer 1

according to this law sum of momentum of two bodies before collision is equal to sum of their momentum after collision. 

DERIVATION 
consider a body of mass (m1) ,moving with initial velocity (u1), when force (f1) is applied to it by 2nd body it's velocity becomes v1 . 
consider a 2nd body of mass(m2) , moving with initial velocity(u2) . when force (f2) is applied to it by 1st body it's velocity becomes v2. 
the time taken is (t) 
WHEN THEY COLLIDE 
f1=m1(v1-u1)/t 

f2=m2(v2-u2)/t 
ACCORDING TO NEWTON'S 3RD LAW 

f1= -f2 

m1(v1-u1)/t = -[ m2(v2-u2)/t] 

m1v1 - m1u1 = -(m2v2-m2u2) [eliminating t] 

m1v1 - m1u1 = -m2v2 +m2u2 

m1v1+m2v2 = m2u2 + m1u1 

now since momentum=mv 
hence , 
sum of initial momentum = sum of final momentuM