Question

two bodies with equal masses move with uniform velocities v and 2v respectively . find the ratio of the kinetic energy .

Answer 1

let two bodies of masses ,
 body x = m
 body y = m     ( because they are equal in mass )
given .
  body x = v
  body y = 2v
 k.e. of x = 1/2mv^2
 k.e. of y = 1/2m(2v)^2
              = $\frac{1}{2} *m *4*v^2$
              = $2mv^2$

ratio = $\frac{K.E.of x}{K.E.of y}$
       = $\frac{ \frac{1*mv^2}{2} }{2mv^2}$
       = 1/4 = 1 : 4 

Answer 2

let,
mass of A = m
mass of B = m  ( given masses are equal )
velocity of body A = v
velocity of body B = 2v
ratio of the bodies = k.e.of A / k.e.of B
                           = 1/2*mv^2 / 1/2*m(2v)^2
                           = 1/4 = 1:4