Question

3. Two bodies with kinetic energies in the ratio of
4:1 are moving with equal linear momentum. The
ratio of their masses is​

Answer 1

we know that ,

K.E = p^2/2m

$K.E1 = \frac{ {p1}^{2} }{2m}$

$K.E2 = \frac{ {p2}^{2} }{2m}$

Given,

linear momentum is same

p1 = p2 = p( say)

Now,

$\frac{K.E1}{K.E2} = \frac{ \frac{ {p}^{2} }{2m1} }{ \frac{ {p}^{2} }{2m2} }$

$\frac{4}{1} = \frac{m2}{m1}$

$\frac{m1}{m2} = \frac{1}{4}$

=> 1: 4