Question

two particles of masses 1kg and 3kg have Kinetic energies in the ratio 1 is to 3 the ratio of the linear momentum is​

Answer 1

Answer:

Let kinetic energy of 1st particle be K1 and that of 2nd particle be K2.

Also, let velocities of 1st and 2nd particles be v and V, respectively.

Given,

K1 : K2 = 1 : 3

K1/K2 = 1/3

OR, 3 K1 = K2 (....i)

Now,

K1 = 1/2 (1kg)(v^2) =v^2/2

P1 = 1 × v = v kgm/s

Now,

K2 = 1/2 (3kg)(V^2) = (3V^2)/2

P2 = 3 × V = 3V kgm/s (...ii)

using (i),

3 k1 = k2

3 (v^2/2) = (3V^2)/2

3v^2 = 3V^2

or, v^2 = V^2

i.e, v = V

Now,

p1 = v kgm/s = V

p2 = 3 V (from ii)

So,

p1/p2 = V/3V =1/3

Therefore,

p1 : p2 = 1 : 3

I hope you understood :)