Question

what is the ratio in the change of momentum if the mass is doubled,mass is halved,mass and velocity incresases by 3 times.....

Answer 1

we are dealing with magnitudes of quantities.
Linear Momentum =  mass * velocity
         initial momentum  = m * v = p  (let)

Change in momentum = m2 * v2  -  m * v

1) mass m2 = 2 * m        velocity = v
                change = 2 m v -  m v = m v = p = initial momentum.

2)  mass is halved .   m2 = m/2
           change = m/2 * v  - m v  = - m v /2  = half of initial momentum

3)  m2 = 3 m       v2 = 3 v
         change =  m2 v2 - m v  =  9 m v - m v = 8 m v
                 is 8 * initial momentum

Answer 2

Let p¹ be d initial momentum and p² be momentum after change in every case 1case P¹= m*v But if mass is doubled then, P²= 2(m)*v P² is directly proportional to m, therefore the 2p¹=p² Hence ratio=2:1 Similarly, 2case Mass is halved the momentum will also bcome half Hence, ratio=1:½ Similarly, Case 3 P¹=m*v P²~3m*3v P²=9mv Hence ratio=9:1