Question

two stones having masses in the ratio of 3:2 ,are dropped from the heights in the ratio 4
:9 , the ratio of magnitudes of their linear momenta just before reaching the ground is (neglect air resistance)
(1) 4:9 (2)2:3
(3) 3:2 (4) 1:1

Answer 1

let final velocity of both particles be v1 and v2
By 3rd equation of motion:
v1^2/v2^2=u1^2+2g*4x/u2^2+2g*9x
Since the particles are dropped their u=0:
v1^2/v2^2=4x/9x
v1/v2=2/3

Now ratio of their momentum
p1/p2=m1*v1/m2*v2
=3y*2/2y*3
=1/1
Therefore ratio of their momentum =1:1